%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA162-1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 06:34:20 PM UTC 2026
% Result : Unsatisfiable 0.44s 0.63s
% Output : Proof 0.91s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA162-1 : TPTP v9.3.0. Released v9.3.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Tue May 5 00:29:40 EDT 2026
% 0.12/0.32 % CPUTime :
% 0.44/0.63 % SZS status Unsatisfiable
% 0.44/0.63 % SZS output start Proof
% 0.44/0.63 tff(r_type, type, (
% 0.44/0.63 r: ( $i * $i ) > $o)).
% 0.44/0.63 tff(elem_1_type, type, (
% 0.44/0.63 elem_1: $i)).
% 0.44/0.63 tff(z_type, type, (
% 0.44/0.63 z: $i)).
% 0.44/0.63 tff(s_type, type, (
% 0.44/0.63 s: $i > $i)).
% 0.44/0.63 tff(inj_0_type, type, (
% 0.44/0.63 inj_0: $i > $i)).
% 0.44/0.63 tff(b_type, type, (
% 0.44/0.63 b: ( $i * $i ) > $o)).
% 0.44/0.63 tff(1,assumption,(z = elem!1), introduced(assumption)).
% 0.44/0.63 tff(2,plain,
% 0.44/0.63 ((elem!1 = z) <=> (z = elem!1)),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(3,plain,
% 0.44/0.63 ((z = elem!1) <=> (elem!1 = z)),
% 0.44/0.63 inference(symmetry,[status(thm)],[2])).
% 0.44/0.63 tff(4,plain,
% 0.44/0.63 (elem!1 = z),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[1, 3])).
% 0.44/0.63 tff(5,assumption,(~(elem!1 = z)), introduced(assumption)).
% 0.44/0.63 tff(6,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[5, 4])).
% 0.44/0.63 tff(7,plain,((~(z = elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.63 tff(8,plain,
% 0.44/0.63 (elem!1 = z),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[7, 1])).
% 0.44/0.63 tff(9,assumption,(elem!1 = z), introduced(assumption)).
% 0.44/0.63 tff(10,plain,
% 0.44/0.63 (s(elem!1) = s(z)),
% 0.44/0.63 inference(monotonicity,[status(thm)],[9])).
% 0.44/0.63 tff(11,assumption,(~(s(elem!1) = s(z))), introduced(assumption)).
% 0.44/0.63 tff(12,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[11, 10])).
% 0.44/0.63 tff(13,plain,((~(elem!1 = z)) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.63 tff(14,plain,
% 0.44/0.63 (s(elem!1) = s(z)),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[13, 8])).
% 0.44/0.63 tff(15,plain,
% 0.44/0.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.44/0.63 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(16,plain,
% 0.44/0.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.44/0.63 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(17,plain,
% 0.44/0.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y)) <=> ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.44/0.63 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(18,axiom,(![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','sinj')).
% 0.44/0.63 tff(19,plain,
% 0.44/0.63 (![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[18, 17])).
% 0.44/0.63 tff(20,plain,(
% 0.44/0.63 ![Y: $i, X: $i] : ((~(s(X) = s(Y))) | (X = Y))),
% 0.44/0.63 inference(skolemize,[status(sab)],[19])).
% 0.44/0.63 tff(21,plain,
% 0.44/0.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[20, 16])).
% 0.44/0.63 tff(22,plain,
% 0.44/0.63 (![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[21, 15])).
% 0.44/0.63 tff(23,plain,
% 0.44/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(z)) = z)),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(24,plain,
% 0.44/0.63 (inj_0(s(z)) = z),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[23, 22])).
% 0.44/0.63 tff(25,assumption,(s(elem!1) = s(z)), introduced(assumption)).
% 0.44/0.63 tff(26,plain,
% 0.44/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(elem!1))) = s(elem!1))),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(27,plain,
% 0.44/0.63 (inj_0(s(s(elem!1))) = s(elem!1)),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[26, 22])).
% 0.44/0.63 tff(28,assumption,(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.44/0.63 tff(29,plain,
% 0.44/0.63 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.44/0.63 inference(symmetry,[status(thm)],[28])).
% 0.44/0.63 tff(30,plain,
% 0.44/0.63 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[29])).
% 0.44/0.63 tff(31,plain,
% 0.44/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1))))))),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(32,plain,
% 0.44/0.63 (inj_0(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(elem!1)))))),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[31, 22])).
% 0.44/0.63 tff(33,plain,
% 0.44/0.63 (s(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.63 inference(symmetry,[status(thm)],[32])).
% 0.44/0.63 tff(34,plain,
% 0.44/0.63 (s(s(s(s(s(elem!1))))) = s(z)),
% 0.44/0.63 inference(transitivity,[status(thm)],[33, 30, 27, 25])).
% 0.44/0.63 tff(35,plain,
% 0.44/0.63 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[34])).
% 0.44/0.63 tff(36,plain,
% 0.44/0.63 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1)))))),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(37,plain,
% 0.44/0.63 (inj_0(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[36, 22])).
% 0.44/0.63 tff(38,plain,
% 0.44/0.63 (s(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.44/0.63 inference(symmetry,[status(thm)],[37])).
% 0.44/0.63 tff(39,plain,
% 0.44/0.63 (s(s(s(s(elem!1)))) = z),
% 0.44/0.63 inference(transitivity,[status(thm)],[38, 35, 24])).
% 0.44/0.63 tff(40,plain,
% 0.44/0.63 (^[X: $i] : refl((~(s(X) = z)) <=> (~(s(X) = z)))),
% 0.44/0.63 inference(bind,[status(th)],[])).
% 0.44/0.63 tff(41,plain,
% 0.44/0.63 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.44/0.63 inference(quant_intro,[status(thm)],[40])).
% 0.44/0.63 tff(42,plain,
% 0.44/0.63 (![X: $i] : (~(s(X) = z)) <=> ![X: $i] : (~(s(X) = z))),
% 0.44/0.63 inference(rewrite,[status(thm)],[])).
% 0.44/0.63 tff(43,axiom,(![X: $i] : (~(s(X) = z))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','snz')).
% 0.44/0.63 tff(44,plain,
% 0.44/0.63 (![X: $i] : (~(s(X) = z))),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[43, 42])).
% 0.44/0.63 tff(45,plain,(
% 0.44/0.63 ![X: $i] : (~(s(X) = z))),
% 0.44/0.63 inference(skolemize,[status(sab)],[44])).
% 0.44/0.63 tff(46,plain,
% 0.44/0.63 (![X: $i] : (~(s(X) = z))),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[45, 41])).
% 0.44/0.63 tff(47,plain,
% 0.44/0.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(elem!1)))) = z))),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(48,plain,
% 0.44/0.63 (~(s(s(s(s(elem!1)))) = z)),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[47, 46])).
% 0.44/0.63 tff(49,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[48, 39])).
% 0.44/0.63 tff(50,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) | (~(s(elem!1) = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.63 tff(51,plain,
% 0.44/0.63 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[50, 14])).
% 0.44/0.63 tff(52,assumption,(~b(s(elem!1), elem!1)), introduced(assumption)).
% 0.44/0.63 tff(53,assumption,(s(z) = elem!1), introduced(assumption)).
% 0.44/0.63 tff(54,plain,
% 0.44/0.63 (s(s(z)) = s(elem!1)),
% 0.44/0.63 inference(monotonicity,[status(thm)],[53])).
% 0.44/0.63 tff(55,plain,
% 0.44/0.63 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 0.44/0.63 inference(monotonicity,[status(thm)],[54])).
% 0.44/0.63 tff(56,plain,
% 0.44/0.63 (b(s(elem!1), elem!1) <=> b(s(s(z)), elem!1)),
% 0.44/0.63 inference(symmetry,[status(thm)],[55])).
% 0.44/0.63 tff(57,plain,
% 0.44/0.63 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(z)), elem!1))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[56])).
% 0.44/0.63 tff(58,plain,
% 0.44/0.63 (~b(s(s(z)), elem!1)),
% 0.44/0.63 inference(modus_ponens,[status(thm)],[52, 57])).
% 0.44/0.63 tff(59,plain,
% 0.44/0.63 ((s(elem!1) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 0.44/0.63 inference(commutativity,[status(thm)],[])).
% 0.44/0.63 tff(60,plain,
% 0.44/0.63 ((s(s(z)) = s(s(elem!1))) <=> (s(elem!1) = s(s(elem!1)))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[54])).
% 0.44/0.63 tff(61,plain,
% 0.44/0.63 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(elem!1))),
% 0.44/0.63 inference(transitivity,[status(thm)],[60, 59])).
% 0.44/0.63 tff(62,plain,
% 0.44/0.63 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(z)) = s(s(elem!1)))),
% 0.44/0.63 inference(symmetry,[status(thm)],[61])).
% 0.44/0.63 tff(63,plain,
% 0.44/0.63 ((~(s(s(elem!1)) = s(elem!1))) <=> (~(s(s(z)) = s(s(elem!1))))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[62])).
% 0.44/0.63 tff(64,assumption,(elem!1 = s(s(elem!1))), introduced(assumption)).
% 0.44/0.63 tff(65,plain,
% 0.44/0.63 (s(z) = s(s(elem!1))),
% 0.44/0.63 inference(transitivity,[status(thm)],[53, 64])).
% 0.44/0.63 tff(66,plain,
% 0.44/0.63 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[65])).
% 0.44/0.63 tff(67,plain,
% 0.44/0.63 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.44/0.63 inference(symmetry,[status(thm)],[66])).
% 0.44/0.63 tff(68,plain,
% 0.44/0.63 (s(elem!1) = inj_0(s(s(elem!1)))),
% 0.44/0.63 inference(symmetry,[status(thm)],[27])).
% 0.44/0.63 tff(69,plain,
% 0.44/0.63 (s(elem!1) = s(s(s(elem!1)))),
% 0.44/0.63 inference(monotonicity,[status(thm)],[64])).
% 0.44/0.63 tff(70,plain,
% 0.44/0.63 (s(s(s(elem!1))) = s(elem!1)),
% 0.44/0.63 inference(symmetry,[status(thm)],[69])).
% 0.44/0.63 tff(71,plain,
% 0.44/0.63 (s(s(s(elem!1))) = z),
% 0.44/0.63 inference(transitivity,[status(thm)],[70, 68, 67, 24])).
% 0.44/0.63 tff(72,plain,
% 0.44/0.63 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(elem!1))) = z))),
% 0.44/0.63 inference(quant_inst,[status(thm)],[])).
% 0.44/0.63 tff(73,plain,
% 0.44/0.63 (~(s(s(s(elem!1))) = z)),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[72, 46])).
% 0.44/0.63 tff(74,plain,
% 0.44/0.63 ($false),
% 0.44/0.63 inference(unit_resolution,[status(thm)],[73, 71])).
% 0.44/0.63 tff(75,plain,((~(s(z) = elem!1)) | (~(elem!1 = s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(76,plain,
% 0.44/0.64 (~(elem!1 = s(s(elem!1)))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[75, 53])).
% 0.44/0.64 tff(77,plain,
% 0.44/0.64 ((elem!1 = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.44/0.64 inference(commutativity,[status(thm)],[])).
% 0.44/0.64 tff(78,plain,
% 0.44/0.64 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(s(elem!1)))),
% 0.44/0.64 inference(symmetry,[status(thm)],[77])).
% 0.44/0.64 tff(79,plain,
% 0.44/0.64 ((s(elem!1) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.44/0.64 inference(commutativity,[status(thm)],[])).
% 0.44/0.64 tff(80,assumption,(s(s(elem!1)) = s(elem!1)), introduced(assumption)).
% 0.44/0.64 tff(81,plain,
% 0.44/0.64 ((s(s(elem!1)) = elem!1) <=> (s(elem!1) = elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[80])).
% 0.44/0.64 tff(82,plain,
% 0.44/0.64 ((s(s(elem!1)) = elem!1) <=> (elem!1 = s(elem!1))),
% 0.44/0.64 inference(transitivity,[status(thm)],[81, 79])).
% 0.44/0.64 tff(83,plain,
% 0.44/0.64 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = elem!1)),
% 0.44/0.64 inference(symmetry,[status(thm)],[82])).
% 0.44/0.64 tff(84,plain,
% 0.44/0.64 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(elem!1)))),
% 0.44/0.64 inference(transitivity,[status(thm)],[83, 78])).
% 0.44/0.64 tff(85,plain,
% 0.44/0.64 (s(elem!1) = s(s(elem!1))),
% 0.44/0.64 inference(symmetry,[status(thm)],[80])).
% 0.44/0.64 tff(86,plain,
% 0.44/0.64 (inj_0(s(elem!1)) = inj_0(s(s(elem!1)))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[85])).
% 0.44/0.64 tff(87,plain,
% 0.44/0.64 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(elem!1)) = elem!1)),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(88,plain,
% 0.44/0.64 (inj_0(s(elem!1)) = elem!1),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[87, 22])).
% 0.44/0.64 tff(89,plain,
% 0.44/0.64 (elem!1 = inj_0(s(elem!1))),
% 0.44/0.64 inference(symmetry,[status(thm)],[88])).
% 0.44/0.64 tff(90,plain,
% 0.44/0.64 (elem!1 = s(elem!1)),
% 0.44/0.64 inference(transitivity,[status(thm)],[89, 86, 27])).
% 0.44/0.64 tff(91,assumption,(~(elem!1 = s(elem!1))), introduced(assumption)).
% 0.44/0.64 tff(92,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[91, 90])).
% 0.44/0.64 tff(93,plain,((~(s(s(elem!1)) = s(elem!1))) | (elem!1 = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(94,plain,
% 0.44/0.64 (elem!1 = s(elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[93, 80])).
% 0.44/0.64 tff(95,plain,
% 0.44/0.64 (elem!1 = s(s(elem!1))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[94, 84])).
% 0.44/0.64 tff(96,assumption,(~(elem!1 = s(s(elem!1)))), introduced(assumption)).
% 0.44/0.64 tff(97,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.44/0.64 tff(98,plain,((~(s(s(elem!1)) = s(elem!1))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(99,plain,
% 0.44/0.64 (~(s(s(elem!1)) = s(elem!1))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[98, 76])).
% 0.44/0.64 tff(100,plain,
% 0.44/0.64 (~(s(s(z)) = s(s(elem!1)))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[99, 63])).
% 0.44/0.64 tff(101,plain,
% 0.44/0.64 (b(s(z), elem!1) <=> b(elem!1, elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[53])).
% 0.44/0.64 tff(102,plain,
% 0.44/0.64 (b(elem!1, elem!1) <=> b(s(z), elem!1)),
% 0.44/0.64 inference(symmetry,[status(thm)],[101])).
% 0.44/0.64 tff(103,plain,
% 0.44/0.64 ((~b(elem!1, elem!1)) <=> (~b(s(z), elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[102])).
% 0.44/0.64 tff(104,plain,
% 0.44/0.64 (^[X: $i] : refl((~b(X, X)) <=> (~b(X, X)))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(105,plain,
% 0.44/0.64 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[104])).
% 0.44/0.64 tff(106,plain,
% 0.44/0.64 (![X: $i] : (~b(X, X)) <=> ![X: $i] : (~b(X, X))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(107,axiom,(![X: $i] : (~b(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','bi')).
% 0.44/0.64 tff(108,plain,
% 0.44/0.64 (![X: $i] : (~b(X, X))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[107, 106])).
% 0.44/0.64 tff(109,plain,(
% 0.44/0.64 ![X: $i] : (~b(X, X))),
% 0.44/0.64 inference(skolemize,[status(sab)],[108])).
% 0.44/0.64 tff(110,plain,
% 0.44/0.64 (![X: $i] : (~b(X, X))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.44/0.64 tff(111,plain,
% 0.44/0.64 ((~![X: $i] : (~b(X, X))) | (~b(elem!1, elem!1))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(112,plain,
% 0.44/0.64 (~b(elem!1, elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[111, 110])).
% 0.44/0.64 tff(113,plain,
% 0.44/0.64 (~b(s(z), elem!1)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[112, 103])).
% 0.44/0.64 tff(114,plain,
% 0.44/0.64 (r(s(z), elem!1) <=> r(elem!1, elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[53])).
% 0.44/0.64 tff(115,plain,
% 0.44/0.64 (r(elem!1, elem!1) <=> r(s(z), elem!1)),
% 0.44/0.64 inference(symmetry,[status(thm)],[114])).
% 0.44/0.64 tff(116,plain,
% 0.44/0.64 ((~r(elem!1, elem!1)) <=> (~r(s(z), elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[115])).
% 0.44/0.64 tff(117,plain,
% 0.44/0.64 (^[X: $i] : refl((~r(X, X)) <=> (~r(X, X)))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(118,plain,
% 0.44/0.64 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[117])).
% 0.44/0.64 tff(119,plain,
% 0.44/0.64 (![X: $i] : (~r(X, X)) <=> ![X: $i] : (~r(X, X))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(120,axiom,(![X: $i] : (~r(X, X))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ri')).
% 0.44/0.64 tff(121,plain,
% 0.44/0.64 (![X: $i] : (~r(X, X))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[120, 119])).
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% 0.44/0.64 inference(skolemize,[status(sab)],[121])).
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% 0.44/0.64 inference(modus_ponens,[status(thm)],[122, 118])).
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% 0.44/0.64 ((~![X: $i] : (~r(X, X))) | (~r(elem!1, elem!1))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
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% 0.44/0.64 inference(unit_resolution,[status(thm)],[124, 123])).
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% 0.44/0.64 (~r(s(z), elem!1)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[125, 116])).
% 0.44/0.64 tff(127,plain,
% 0.44/0.64 ((elem!1 = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.44/0.64 inference(commutativity,[status(thm)],[])).
% 0.44/0.64 tff(128,assumption,(~r(s(z), elem!1)), introduced(assumption)).
% 0.44/0.64 tff(129,assumption,(~b(s(z), elem!1)), introduced(assumption)).
% 0.44/0.64 tff(130,plain,
% 0.44/0.64 (^[Y: $i, X: $i] : refl(((X = Y) | b(X, Y) | r(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(131,plain,
% 0.44/0.64 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[130])).
% 0.44/0.64 tff(132,plain,
% 0.44/0.64 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(133,plain,
% 0.44/0.64 (^[Y: $i, X: $i] : rewrite((((X = Y) | r(X, Y)) | b(X, Y)) <=> ((X = Y) | b(X, Y) | r(X, Y)))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(134,plain,
% 0.44/0.64 (![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y)) <=> ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[133])).
% 0.44/0.64 tff(135,axiom,(![Y: $i, X: $i] : (((X = Y) | r(X, Y)) | b(X, Y))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','rb')).
% 0.44/0.64 tff(136,plain,
% 0.44/0.64 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[135, 134])).
% 0.44/0.64 tff(137,plain,
% 0.44/0.64 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[136, 132])).
% 0.44/0.64 tff(138,plain,(
% 0.44/0.64 ![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(skolemize,[status(sab)],[137])).
% 0.44/0.64 tff(139,plain,
% 0.44/0.64 (![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[138, 131])).
% 0.44/0.64 tff(140,plain,
% 0.44/0.64 (((~![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))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(141,plain,
% 0.44/0.64 ((~![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))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(142,plain,
% 0.44/0.64 ((~![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)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[141, 140])).
% 0.44/0.64 tff(143,plain,
% 0.44/0.64 ((s(z) = elem!1) | b(s(z), elem!1) | r(s(z), elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[142, 139])).
% 0.44/0.64 tff(144,plain,
% 0.44/0.64 (s(z) = elem!1),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[143, 129, 128])).
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% 0.44/0.64 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[144])).
% 0.44/0.64 tff(146,plain,
% 0.44/0.64 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.44/0.64 inference(transitivity,[status(thm)],[145, 127])).
% 0.44/0.64 tff(147,plain,
% 0.44/0.64 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[146])).
% 0.44/0.64 tff(148,assumption,(s(z) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
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% 0.44/0.64 inference(symmetry,[status(thm)],[148])).
% 0.44/0.64 tff(150,plain,
% 0.44/0.64 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(z))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[149])).
% 0.44/0.64 tff(151,plain,
% 0.44/0.64 (s(s(s(s(s(elem!1))))) = z),
% 0.44/0.64 inference(transitivity,[status(thm)],[33, 150, 24])).
% 0.44/0.64 tff(152,plain,
% 0.44/0.64 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(elem!1))))) = z))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(153,plain,
% 0.44/0.64 (~(s(s(s(s(s(elem!1))))) = z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[152, 46])).
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% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[153, 151])).
% 0.44/0.64 tff(155,plain,(~(s(z) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(156,plain,
% 0.44/0.64 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[155, 147])).
% 0.44/0.64 tff(157,plain,
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% 0.44/0.64 inference(transitivity,[status(thm)],[33, 30, 27])).
% 0.44/0.64 tff(158,plain,
% 0.44/0.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[157])).
% 0.44/0.64 tff(159,plain,
% 0.44/0.64 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.44/0.64 inference(symmetry,[status(thm)],[158])).
% 0.44/0.64 tff(160,plain,
% 0.44/0.64 (s(z) = s(s(s(s(elem!1))))),
% 0.44/0.64 inference(transitivity,[status(thm)],[53, 89, 159, 37])).
% 0.44/0.64 tff(161,plain,
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% 0.44/0.64 inference(monotonicity,[status(thm)],[160])).
% 0.44/0.64 tff(162,plain,
% 0.44/0.64 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(z))),
% 0.44/0.64 inference(symmetry,[status(thm)],[161])).
% 0.44/0.64 tff(163,plain,
% 0.44/0.64 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1))))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(164,plain,
% 0.44/0.64 (inj_0(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[163, 22])).
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% 0.44/0.64 inference(symmetry,[status(thm)],[164])).
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% 0.44/0.64 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[28])).
% 0.44/0.64 tff(167,plain,
% 0.44/0.64 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.44/0.64 inference(symmetry,[status(thm)],[166])).
% 0.44/0.64 tff(168,plain,
% 0.44/0.64 (s(s(s(s(s(s(s(elem!1))))))) = z),
% 0.44/0.64 inference(transitivity,[status(thm)],[167, 165, 162, 24])).
% 0.44/0.64 tff(169,plain,
% 0.44/0.64 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(elem!1))))))) = z))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(170,plain,
% 0.44/0.64 (~(s(s(s(s(s(s(s(elem!1))))))) = z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[169, 46])).
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% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[170, 168])).
% 0.44/0.64 tff(172,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(173,plain,
% 0.44/0.64 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[172, 144])).
% 0.44/0.64 tff(174,plain,
% 0.44/0.64 ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.64 inference(commutativity,[status(thm)],[])).
% 0.44/0.64 tff(175,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))), introduced(assumption)).
% 0.44/0.64 tff(176,plain,
% 0.44/0.64 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.44/0.64 tff(177,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.44/0.64 tff(178,plain,
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% 0.44/0.64 inference(unit_resolution,[status(thm)],[177, 176])).
% 0.44/0.64 tff(179,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(180,plain,
% 0.44/0.64 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[179, 173])).
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% 0.44/0.64 inference(monotonicity,[status(thm)],[144])).
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% 0.44/0.64 inference(monotonicity,[status(thm)],[181])).
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% 0.44/0.64 (b(elem!1, s(s(s(z)))) <=> b(elem!1, s(s(elem!1)))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[182])).
% 0.44/0.64 tff(184,plain,
% 0.44/0.64 ((s(z) = s(s(s(z)))) <=> (elem!1 = s(s(s(z))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[144])).
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% 0.44/0.64 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(z)))) = s(s(z)))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
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% 0.44/0.64 tff(194,plain,
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% 0.44/0.64 inference(unit_resolution,[status(thm)],[193, 46])).
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% 0.44/0.64 tff(196,plain,(~(s(z) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(197,plain,
% 0.44/0.64 (~(elem!1 = s(s(s(z))))),
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% 0.44/0.64 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
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% 0.44/0.64 (r(s(s(z)), elem!1) <=> r(s(elem!1), s(z))),
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% 0.44/0.64 tff(203,assumption,(~(s(s(z)) = s(s(elem!1)))), introduced(assumption)).
% 0.44/0.64 tff(204,assumption,(s(s(z)) = elem!1), introduced(assumption)).
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% 0.44/0.64 ((s(z) = s(s(z))) <=> (s(z) = elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[204])).
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% 0.44/0.64 ((s(z) = elem!1) <=> (s(z) = s(s(z)))),
% 0.44/0.64 inference(symmetry,[status(thm)],[205])).
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% 0.44/0.64 tff(208,plain,
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% 0.44/0.64 inference(symmetry,[status(thm)],[207])).
% 0.44/0.64 tff(209,plain,
% 0.44/0.64 (s(s(z)) = s(s(s(s(s(s(elem!1))))))),
% 0.44/0.64 inference(transitivity,[status(thm)],[204, 208])).
% 0.44/0.64 tff(210,plain,
% 0.44/0.64 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[209])).
% 0.44/0.64 tff(211,plain,
% 0.44/0.64 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(z))) = s(z))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(212,plain,
% 0.44/0.64 (inj_0(s(s(z))) = s(z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[211, 22])).
% 0.44/0.64 tff(213,plain,
% 0.44/0.64 (s(z) = inj_0(s(s(z)))),
% 0.44/0.64 inference(symmetry,[status(thm)],[212])).
% 0.44/0.64 tff(214,plain,
% 0.44/0.64 (s(z) = s(s(s(s(s(elem!1)))))),
% 0.44/0.64 inference(transitivity,[status(thm)],[213, 210, 32])).
% 0.44/0.64 tff(215,plain,
% 0.44/0.64 (inj_0(s(z)) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[214])).
% 0.44/0.64 tff(216,plain,
% 0.44/0.64 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 0.44/0.64 inference(symmetry,[status(thm)],[215])).
% 0.44/0.64 tff(217,plain,
% 0.44/0.64 (s(s(s(s(elem!1)))) = z),
% 0.44/0.64 inference(transitivity,[status(thm)],[38, 216, 24])).
% 0.44/0.64 tff(218,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[48, 217])).
% 0.44/0.64 tff(219,plain,((~(s(s(z)) = elem!1)) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(220,plain,
% 0.44/0.64 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[219, 204])).
% 0.44/0.64 tff(221,assumption,(~(s(s(s(s(s(s(elem!1)))))) = elem!1)), introduced(assumption)).
% 0.44/0.64 tff(222,assumption,(s(s(elem!1)) = elem!1), introduced(assumption)).
% 0.44/0.64 tff(223,plain,
% 0.44/0.64 (s(s(s(elem!1))) = s(elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[222])).
% 0.44/0.64 tff(224,plain,
% 0.44/0.64 (s(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[223])).
% 0.44/0.64 tff(225,plain,
% 0.44/0.64 (s(s(s(s(elem!1)))) = elem!1),
% 0.44/0.64 inference(transitivity,[status(thm)],[224, 222])).
% 0.44/0.64 tff(226,plain,
% 0.44/0.64 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[225])).
% 0.44/0.64 tff(227,plain,
% 0.44/0.64 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[226])).
% 0.44/0.64 tff(228,plain,
% 0.44/0.64 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.44/0.64 inference(transitivity,[status(thm)],[227, 222])).
% 0.44/0.64 tff(229,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[221, 228])).
% 0.44/0.64 tff(230,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(231,plain,
% 0.44/0.64 (~(s(s(elem!1)) = elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[230, 221])).
% 0.44/0.64 tff(232,plain,
% 0.44/0.64 (s(s(elem!1)) = elem!1),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[64, 77])).
% 0.44/0.64 tff(233,assumption,(~(s(s(elem!1)) = elem!1)), introduced(assumption)).
% 0.44/0.64 tff(234,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[233, 232])).
% 0.44/0.64 tff(235,plain,((~(elem!1 = s(s(elem!1)))) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(236,plain,
% 0.44/0.64 (~(elem!1 = s(s(elem!1)))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[235, 231])).
% 0.44/0.64 tff(237,plain,
% 0.44/0.64 (~(s(s(elem!1)) = s(elem!1))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[98, 236])).
% 0.44/0.64 tff(238,assumption,(s(elem!1) = elem!1), introduced(assumption)).
% 0.44/0.64 tff(239,plain,
% 0.44/0.64 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(elem!1)) = elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[238])).
% 0.44/0.64 tff(240,plain,
% 0.44/0.64 ((s(s(elem!1)) = elem!1) <=> (s(s(elem!1)) = s(elem!1))),
% 0.44/0.64 inference(symmetry,[status(thm)],[239])).
% 0.44/0.64 tff(241,plain,
% 0.44/0.64 (s(s(elem!1)) = s(elem!1)),
% 0.44/0.64 inference(monotonicity,[status(thm)],[238])).
% 0.44/0.64 tff(242,plain,
% 0.44/0.64 (s(s(elem!1)) = elem!1),
% 0.44/0.64 inference(transitivity,[status(thm)],[241, 238])).
% 0.44/0.64 tff(243,plain,
% 0.44/0.64 (s(s(elem!1)) = s(elem!1)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[242, 240])).
% 0.44/0.64 tff(244,assumption,(~(s(s(elem!1)) = s(elem!1))), introduced(assumption)).
% 0.44/0.64 tff(245,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[244, 243])).
% 0.44/0.64 tff(246,plain,((~(s(elem!1) = elem!1)) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(247,plain,
% 0.44/0.64 (~(s(elem!1) = elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[246, 237])).
% 0.44/0.64 tff(248,assumption,(~(s(elem!1) = s(s(z)))), introduced(assumption)).
% 0.44/0.64 tff(249,plain,
% 0.44/0.64 (s(elem!1) = s(s(z))),
% 0.44/0.64 inference(symmetry,[status(thm)],[54])).
% 0.44/0.64 tff(250,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[248, 249])).
% 0.44/0.64 tff(251,plain,((~(s(z) = elem!1)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(252,plain,
% 0.44/0.64 (~(s(z) = elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[251, 248])).
% 0.44/0.64 tff(253,assumption,(b(s(z), elem!1)), introduced(assumption)).
% 0.44/0.64 tff(254,assumption,(r(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.44/0.64 tff(255,plain,
% 0.44/0.64 (s(s(elem!1)) = s(s(z))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[25])).
% 0.44/0.64 tff(256,plain,
% 0.44/0.64 (s(s(z)) = s(s(elem!1))),
% 0.44/0.64 inference(symmetry,[status(thm)],[255])).
% 0.44/0.64 tff(257,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[203, 256])).
% 0.44/0.64 tff(258,plain,((~(s(elem!1) = s(z))) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(259,plain,
% 0.44/0.64 (~(s(elem!1) = s(z))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[258, 203])).
% 0.44/0.64 tff(260,plain,
% 0.44/0.64 (~(elem!1 = z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[13, 259])).
% 0.44/0.64 tff(261,plain,
% 0.44/0.64 (~(z = elem!1)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[7, 260])).
% 0.44/0.64 tff(262,assumption,(b(z, elem!1)), introduced(assumption)).
% 0.44/0.64 tff(263,plain,
% 0.44/0.64 (^[X0: $i, X3: $i, X2: $i, X1: $i] : refl(((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(264,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[263])).
% 0.44/0.64 tff(265,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(266,plain,
% 0.44/0.64 (^[X0: $i, X3: $i, X2: $i, X1: $i] : trans(monotonicity(trans(monotonicity(rewrite(((~b(X0, X1)) | (~b(X1, X2))) <=> ((~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> (((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))))), rewrite((((~b(X1, X2)) | (~b(X0, X1))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) <=> ((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> (((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))))), rewrite((((~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))), (((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))))),
% 0.44/0.64 inference(bind,[status(th)],[])).
% 0.44/0.64 tff(267,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3))) <=> ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(quant_intro,[status(thm)],[266])).
% 0.44/0.64 tff(268,axiom,(![X0: $i, X3: $i, X2: $i, X1: $i] : ((((~b(X0, X1)) | (~b(X1, X2))) | (~b(X0, X3))) | (~b(X1, X3)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axb')).
% 0.44/0.64 tff(269,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[268, 267])).
% 0.44/0.64 tff(270,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[269, 265])).
% 0.44/0.64 tff(271,plain,(
% 0.44/0.64 ![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(skolemize,[status(sab)],[270])).
% 0.44/0.64 tff(272,plain,
% 0.44/0.64 (![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[271, 264])).
% 0.44/0.64 tff(273,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(274,plain,
% 0.44/0.64 (((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z))) <=> ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(275,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[274])).
% 0.44/0.64 tff(276,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.64 inference(transitivity,[status(thm)],[275, 273])).
% 0.44/0.64 tff(277,plain,
% 0.44/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), z)))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(278,plain,
% 0.44/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[277, 276])).
% 0.44/0.64 tff(279,plain,
% 0.44/0.64 ((~b(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[278, 272])).
% 0.44/0.64 tff(280,plain,
% 0.44/0.64 (~b(s(z), z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[279, 262, 253])).
% 0.44/0.64 tff(281,assumption,(~r(s(z), z)), introduced(assumption)).
% 0.44/0.64 tff(282,assumption,(~b(s(z), z)), introduced(assumption)).
% 0.44/0.64 tff(283,plain,
% 0.44/0.64 ((~![X: $i] : (~(s(X) = z))) | (~(s(z) = z))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(284,plain,
% 0.44/0.64 (~(s(z) = z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[283, 46])).
% 0.44/0.64 tff(285,plain,
% 0.44/0.64 (((~![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))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(286,plain,
% 0.44/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = z) | b(s(z), z) | r(s(z), z))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(287,plain,
% 0.44/0.64 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = z) | b(s(z), z) | r(s(z), z)),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[286, 285])).
% 0.44/0.64 tff(288,plain,
% 0.44/0.64 ($false),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[287, 139, 284, 282, 281])).
% 0.44/0.64 tff(289,plain,(b(s(z), z) | r(s(z), z)), inference(lemma,lemma(discharge,[]))).
% 0.44/0.64 tff(290,plain,
% 0.44/0.64 (r(s(z), z)),
% 0.44/0.64 inference(unit_resolution,[status(thm)],[289, 280])).
% 0.44/0.64 tff(291,assumption,(b(s(elem!1), elem!1)), introduced(assumption)).
% 0.44/0.64 tff(292,plain,
% 0.44/0.64 ((s(z) = s(elem!1)) <=> (s(elem!1) = s(z))),
% 0.44/0.64 inference(commutativity,[status(thm)],[])).
% 0.44/0.64 tff(293,plain,
% 0.44/0.64 ((s(elem!1) = s(z)) <=> (s(z) = s(elem!1))),
% 0.44/0.64 inference(symmetry,[status(thm)],[292])).
% 0.44/0.64 tff(294,plain,
% 0.44/0.64 ((~(s(elem!1) = s(z))) <=> (~(s(z) = s(elem!1)))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[293])).
% 0.44/0.64 tff(295,plain,
% 0.44/0.64 (~(s(z) = s(elem!1))),
% 0.44/0.64 inference(modus_ponens,[status(thm)],[259, 294])).
% 0.44/0.64 tff(296,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(297,plain,
% 0.44/0.64 (((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.44/0.64 inference(rewrite,[status(thm)],[])).
% 0.44/0.64 tff(298,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))))),
% 0.44/0.64 inference(monotonicity,[status(thm)],[297])).
% 0.44/0.64 tff(299,plain,
% 0.44/0.64 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.44/0.64 inference(transitivity,[status(thm)],[298, 296])).
% 0.44/0.64 tff(300,plain,
% 0.44/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1))))),
% 0.44/0.64 inference(quant_inst,[status(thm)],[])).
% 0.44/0.64 tff(301,plain,
% 0.44/0.64 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), s(elem!1)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[300, 299])).
% 0.44/0.65 tff(302,plain,
% 0.44/0.65 (~b(s(z), s(elem!1))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[301, 272, 253, 291])).
% 0.44/0.65 tff(303,plain,
% 0.44/0.65 (((~![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)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(304,plain,
% 0.44/0.65 ((~![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)))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(305,plain,
% 0.44/0.65 ((~![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))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[304, 303])).
% 0.44/0.65 tff(306,plain,
% 0.44/0.65 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[305, 139, 302])).
% 0.44/0.65 tff(307,plain,
% 0.44/0.65 (r(s(z), s(elem!1))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[306, 295])).
% 0.44/0.65 tff(308,assumption,(b(s(elem!1), s(z))), introduced(assumption)).
% 0.44/0.65 tff(309,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(310,plain,
% 0.44/0.65 (((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(311,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[310])).
% 0.44/0.65 tff(312,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z))))),
% 0.44/0.65 inference(transitivity,[status(thm)],[311, 309])).
% 0.44/0.65 tff(313,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (~b(s(elem!1), s(z))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(314,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.44/0.65 tff(315,plain,
% 0.44/0.65 ($false),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[314, 272, 253, 291, 308])).
% 0.44/0.65 tff(316,plain,((~b(s(z), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.65 tff(317,plain,
% 0.44/0.65 (~b(s(elem!1), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[316, 291, 253])).
% 0.44/0.65 tff(318,assumption,(~r(s(elem!1), s(z))), introduced(assumption)).
% 0.44/0.65 tff(319,assumption,(~b(s(elem!1), s(z))), introduced(assumption)).
% 0.44/0.65 tff(320,plain,
% 0.44/0.65 (((~![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)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(321,plain,
% 0.44/0.65 ((~![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)))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(322,plain,
% 0.44/0.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(z)) | b(s(elem!1), s(z)) | r(s(elem!1), s(z))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[321, 320])).
% 0.44/0.65 tff(323,plain,
% 0.44/0.65 ($false),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[322, 139, 11, 319, 318])).
% 0.44/0.65 tff(324,plain,(r(s(elem!1), s(z)) | (s(elem!1) = s(z)) | b(s(elem!1), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.65 tff(325,plain,
% 0.44/0.65 (r(s(elem!1), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[324, 317, 259])).
% 0.44/0.65 tff(326,assumption,(b(s(s(z)), elem!1)), introduced(assumption)).
% 0.44/0.65 tff(327,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(328,plain,
% 0.44/0.65 (((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(329,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[328])).
% 0.44/0.65 tff(330,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1)))),
% 0.44/0.65 inference(transitivity,[status(thm)],[329, 327])).
% 0.44/0.65 tff(331,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(332,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), elem!1))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[331, 330])).
% 0.44/0.65 tff(333,plain,
% 0.44/0.65 (~b(s(elem!1), s(s(z)))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[332, 272, 326, 291])).
% 0.44/0.65 tff(334,plain,
% 0.44/0.65 (((~![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))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(335,plain,
% 0.44/0.65 ((~![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))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(336,plain,
% 0.44/0.65 ((~![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)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[335, 334])).
% 0.44/0.65 tff(337,plain,
% 0.44/0.65 (r(s(elem!1), s(s(z)))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[336, 139, 248, 333])).
% 0.44/0.65 tff(338,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(339,plain,
% 0.44/0.65 (((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(340,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[339])).
% 0.44/0.65 tff(341,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 0.44/0.65 inference(transitivity,[status(thm)],[340, 338])).
% 0.44/0.65 tff(342,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(343,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), s(z)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[342, 341])).
% 0.44/0.65 tff(344,plain,
% 0.44/0.65 (~b(s(s(z)), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[343, 272, 326, 253])).
% 0.44/0.65 tff(345,plain,
% 0.44/0.65 ((s(s(z)) = s(z)) <=> (s(z) = s(s(z)))),
% 0.44/0.65 inference(commutativity,[status(thm)],[])).
% 0.44/0.65 tff(346,plain,
% 0.44/0.65 ((s(z) = s(s(z))) <=> (s(s(z)) = s(z))),
% 0.44/0.65 inference(symmetry,[status(thm)],[345])).
% 0.44/0.65 tff(347,plain,
% 0.44/0.65 ((~(s(z) = s(s(z)))) <=> (~(s(s(z)) = s(z)))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[346])).
% 0.44/0.65 tff(348,assumption,(s(z) = s(s(z))), introduced(assumption)).
% 0.44/0.65 tff(349,plain,
% 0.44/0.65 (inj_0(s(z)) = inj_0(s(s(z)))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[348])).
% 0.44/0.65 tff(350,plain,
% 0.44/0.65 (inj_0(s(s(z))) = inj_0(s(z))),
% 0.44/0.65 inference(symmetry,[status(thm)],[349])).
% 0.44/0.65 tff(351,plain,
% 0.44/0.65 (s(z) = z),
% 0.44/0.65 inference(transitivity,[status(thm)],[213, 350, 24])).
% 0.44/0.65 tff(352,plain,
% 0.44/0.65 ($false),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[284, 351])).
% 0.44/0.65 tff(353,plain,(~(s(z) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.65 tff(354,plain,
% 0.44/0.65 (~(s(s(z)) = s(z))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[353, 347])).
% 0.44/0.65 tff(355,plain,
% 0.44/0.65 (((~![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)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(356,plain,
% 0.44/0.65 ((~![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)))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(357,plain,
% 0.44/0.65 ((~![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))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[356, 355])).
% 0.44/0.65 tff(358,plain,
% 0.44/0.65 ((s(s(z)) = s(z)) | b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[357, 139])).
% 0.44/0.65 tff(359,plain,
% 0.44/0.65 (b(s(s(z)), s(z)) | r(s(s(z)), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[358, 354])).
% 0.44/0.65 tff(360,plain,
% 0.44/0.65 (r(s(s(z)), s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[359, 344])).
% 0.44/0.65 tff(361,assumption,(r(s(elem!1), s(z))), introduced(assumption)).
% 0.44/0.65 tff(362,plain,
% 0.44/0.65 (^[X0: $i, X2: $i, X1: $i] : refl(((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.44/0.65 inference(bind,[status(th)],[])).
% 0.44/0.65 tff(363,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(quant_intro,[status(thm)],[362])).
% 0.44/0.65 tff(364,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(365,plain,
% 0.44/0.65 (^[X0: $i, X2: $i, X1: $i] : rewrite((((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1))))),
% 0.44/0.65 inference(bind,[status(th)],[])).
% 0.44/0.65 tff(366,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2))) <=> ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(quant_intro,[status(thm)],[365])).
% 0.44/0.65 tff(367,axiom,(![X0: $i, X2: $i, X1: $i] : (((~r(X0, X1)) | (~r(X0, X2))) | (~r(X1, X2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','axr')).
% 0.44/0.65 tff(368,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[367, 366])).
% 0.44/0.65 tff(369,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[368, 364])).
% 0.44/0.65 tff(370,plain,(
% 0.44/0.65 ![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(skolemize,[status(sab)],[369])).
% 0.44/0.65 tff(371,plain,
% 0.44/0.65 (![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[370, 363])).
% 0.44/0.65 tff(372,plain,
% 0.44/0.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(373,plain,
% 0.44/0.65 (((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(374,plain,
% 0.44/0.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[373])).
% 0.44/0.65 tff(375,plain,
% 0.44/0.65 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z))))),
% 0.44/0.65 inference(transitivity,[status(thm)],[374, 372])).
% 0.44/0.65 tff(376,plain,
% 0.44/0.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), s(s(z)))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(377,plain,
% 0.44/0.65 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(elem!1), s(s(z)))) | (~r(s(elem!1), s(z)))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[376, 375])).
% 0.44/0.65 tff(378,plain,
% 0.44/0.65 ($false),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[377, 371, 361, 360, 337])).
% 0.44/0.65 tff(379,plain,((~b(s(s(z)), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~b(s(z), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.65 tff(380,plain,
% 0.44/0.65 (~b(s(s(z)), elem!1)),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[379, 325, 248, 253, 291])).
% 0.44/0.65 tff(381,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(382,plain,
% 0.44/0.65 (((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(383,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[382])).
% 0.44/0.65 tff(384,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.65 inference(transitivity,[status(thm)],[383, 381])).
% 0.44/0.65 tff(385,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(z, s(z))))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(386,plain,
% 0.44/0.65 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.44/0.65 tff(387,plain,
% 0.44/0.65 ((~b(z, s(z))) | (~b(z, elem!1)) | (~b(s(z), elem!1))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[386, 272])).
% 0.44/0.65 tff(388,plain,
% 0.44/0.65 (~b(z, s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[387, 262, 253])).
% 0.44/0.65 tff(389,plain,
% 0.44/0.65 ((z = s(z)) <=> (s(z) = z)),
% 0.44/0.65 inference(commutativity,[status(thm)],[])).
% 0.44/0.65 tff(390,plain,
% 0.44/0.65 ((s(z) = z) <=> (z = s(z))),
% 0.44/0.65 inference(symmetry,[status(thm)],[389])).
% 0.44/0.65 tff(391,plain,
% 0.44/0.65 ((~(s(z) = z)) <=> (~(z = s(z)))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[390])).
% 0.44/0.65 tff(392,plain,
% 0.44/0.65 (~(z = s(z))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[284, 391])).
% 0.44/0.65 tff(393,plain,
% 0.44/0.65 (((~![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)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(394,plain,
% 0.44/0.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(z)) | b(z, s(z)) | r(z, s(z)))),
% 0.44/0.65 inference(quant_inst,[status(thm)],[])).
% 0.44/0.65 tff(395,plain,
% 0.44/0.65 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.44/0.65 inference(modus_ponens,[status(thm)],[394, 393])).
% 0.44/0.65 tff(396,plain,
% 0.44/0.65 ((z = s(z)) | b(z, s(z)) | r(z, s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[395, 139])).
% 0.44/0.65 tff(397,plain,
% 0.44/0.65 (b(z, s(z)) | r(z, s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[396, 392])).
% 0.44/0.65 tff(398,plain,
% 0.44/0.65 (r(z, s(z))),
% 0.44/0.65 inference(unit_resolution,[status(thm)],[397, 388])).
% 0.44/0.65 tff(399,assumption,(b(s(elem!1), z)), introduced(assumption)).
% 0.44/0.65 tff(400,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(401,plain,
% 0.44/0.65 (((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z))) <=> ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 0.44/0.65 inference(rewrite,[status(thm)],[])).
% 0.44/0.65 tff(402,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))))),
% 0.44/0.65 inference(monotonicity,[status(thm)],[401])).
% 0.44/0.65 tff(403,plain,
% 0.44/0.65 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1)))),
% 0.44/0.66 inference(transitivity,[status(thm)],[402, 400])).
% 0.44/0.66 tff(404,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), z)))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(405,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.44/0.66 tff(406,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[405, 272, 262, 399, 291])).
% 0.44/0.66 tff(407,plain,((~b(z, elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(408,plain,
% 0.44/0.66 (~b(s(elem!1), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[407, 262, 291])).
% 0.44/0.66 tff(409,plain,
% 0.44/0.66 ((~![X: $i] : (~(s(X) = z))) | (~(s(elem!1) = z))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(410,plain,
% 0.44/0.66 (~(s(elem!1) = z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[409, 46])).
% 0.44/0.66 tff(411,plain,
% 0.44/0.66 (((~![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))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(412,plain,
% 0.44/0.66 ((~![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))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(413,plain,
% 0.44/0.66 ((~![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)),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[412, 411])).
% 0.44/0.66 tff(414,plain,
% 0.44/0.66 (b(s(elem!1), z) | r(s(elem!1), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[413, 139, 410])).
% 0.44/0.66 tff(415,plain,
% 0.44/0.66 (r(s(elem!1), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[414, 408])).
% 0.44/0.66 tff(416,assumption,(r(s(elem!1), z)), introduced(assumption)).
% 0.44/0.66 tff(417,assumption,(r(z, s(z))), introduced(assumption)).
% 0.44/0.66 tff(418,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(419,plain,
% 0.44/0.66 (((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z))) <=> ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(420,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[419])).
% 0.44/0.66 tff(421,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.44/0.66 inference(transitivity,[status(thm)],[420, 418])).
% 0.44/0.66 tff(422,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), z)))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(423,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.44/0.66 tff(424,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[423, 371, 417, 416, 361])).
% 0.44/0.66 tff(425,plain,((~r(z, s(z))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(426,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[425, 415, 398, 361])).
% 0.44/0.66 tff(427,plain,((~b(z, elem!1)) | (~r(s(elem!1), s(z))) | (~b(s(elem!1), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(428,plain,
% 0.44/0.66 (~b(z, elem!1)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[427, 325, 291, 253])).
% 0.44/0.66 tff(429,plain,
% 0.44/0.66 (((~![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))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(430,plain,
% 0.44/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = elem!1) | b(z, elem!1) | r(z, elem!1))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(431,plain,
% 0.44/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[430, 429])).
% 0.44/0.66 tff(432,plain,
% 0.44/0.66 ((z = elem!1) | b(z, elem!1) | r(z, elem!1)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[431, 139])).
% 0.44/0.66 tff(433,plain,
% 0.44/0.66 (r(z, elem!1)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[432, 428, 261])).
% 0.44/0.66 tff(434,assumption,(r(s(s(z)), elem!1)), introduced(assumption)).
% 0.44/0.66 tff(435,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(436,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(437,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(elem!1))))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[436, 435])).
% 0.44/0.66 tff(438,plain,
% 0.44/0.66 (~r(s(s(z)), s(s(elem!1)))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[437, 371, 434, 254])).
% 0.44/0.66 tff(439,plain,
% 0.44/0.66 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(440,plain,
% 0.44/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1))))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(441,plain,
% 0.44/0.66 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(z)) = s(s(elem!1))) | b(s(s(z)), s(s(elem!1))) | r(s(s(z)), s(s(elem!1)))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[440, 439])).
% 0.44/0.66 tff(442,plain,
% 0.44/0.66 (b(s(s(z)), s(s(elem!1)))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[441, 139, 203, 438])).
% 0.44/0.66 tff(443,assumption,(r(z, elem!1)), introduced(assumption)).
% 0.44/0.66 tff(444,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(445,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z)))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(446,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), z))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[445, 444])).
% 0.44/0.66 tff(447,plain,
% 0.44/0.66 (~r(s(s(elem!1)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[446, 371, 443, 254])).
% 0.44/0.66 tff(448,plain,
% 0.44/0.66 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(elem!1)) = z))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(449,plain,
% 0.44/0.66 (~(s(s(elem!1)) = z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[448, 46])).
% 0.44/0.66 tff(450,plain,
% 0.44/0.66 (((~![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))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(451,plain,
% 0.44/0.66 ((~![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))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(452,plain,
% 0.44/0.66 ((~![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)),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[451, 450])).
% 0.44/0.66 tff(453,plain,
% 0.44/0.66 (b(s(s(elem!1)), z) | r(s(s(elem!1)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[452, 139, 449])).
% 0.44/0.66 tff(454,plain,
% 0.44/0.66 (b(s(s(elem!1)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[453, 447])).
% 0.44/0.66 tff(455,plain,
% 0.44/0.66 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(456,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z)))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(457,plain,
% 0.44/0.66 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.44/0.66 tff(458,plain,
% 0.44/0.66 (~r(s(s(z)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[457, 371, 443, 434])).
% 0.44/0.66 tff(459,plain,
% 0.44/0.66 (((~![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))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(460,plain,
% 0.44/0.66 ((~![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))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(461,plain,
% 0.44/0.66 ((~![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)),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[460, 459])).
% 0.44/0.66 tff(462,plain,
% 0.44/0.66 (b(s(s(z)), z) | r(s(s(z)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[461, 139, 194])).
% 0.44/0.66 tff(463,plain,
% 0.44/0.66 (b(s(s(z)), z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[462, 458])).
% 0.44/0.66 tff(464,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(465,plain,
% 0.44/0.66 (((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(466,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[465])).
% 0.44/0.66 tff(467,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.44/0.66 inference(transitivity,[status(thm)],[466, 464])).
% 0.44/0.66 tff(468,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(z)), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(469,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[468, 467])).
% 0.44/0.66 tff(470,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[469, 272, 463, 454, 442])).
% 0.44/0.66 tff(471,plain,((~r(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(472,plain,
% 0.44/0.66 (~r(s(s(z)), elem!1)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[471, 433, 254, 203])).
% 0.44/0.66 tff(473,plain,
% 0.44/0.66 (((~![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))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(474,plain,
% 0.44/0.66 ((~![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))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(475,plain,
% 0.44/0.66 ((~![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)),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[474, 473])).
% 0.44/0.66 tff(476,plain,
% 0.44/0.66 ((s(s(z)) = elem!1) | b(s(s(z)), elem!1) | r(s(s(z)), elem!1)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[475, 139])).
% 0.44/0.66 tff(477,plain,
% 0.44/0.66 (s(s(z)) = elem!1),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[476, 472, 380])).
% 0.44/0.66 tff(478,assumption,(s(elem!1) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.44/0.66 tff(479,plain,
% 0.44/0.66 (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[478])).
% 0.44/0.66 tff(480,plain,
% 0.44/0.66 (s(s(s(elem!1))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[479])).
% 0.44/0.66 tff(481,plain,
% 0.44/0.66 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[480])).
% 0.44/0.66 tff(482,plain,
% 0.44/0.66 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[478])).
% 0.44/0.66 tff(483,plain,
% 0.44/0.66 (s(s(z)) = s(s(s(s(s(elem!1)))))),
% 0.44/0.66 inference(transitivity,[status(thm)],[204, 89, 482, 32])).
% 0.44/0.66 tff(484,plain,
% 0.44/0.66 (inj_0(s(s(z))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[483])).
% 0.44/0.66 tff(485,plain,
% 0.44/0.66 (s(z) = s(s(s(s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.66 inference(transitivity,[status(thm)],[213, 484, 37, 481])).
% 0.44/0.66 tff(486,plain,
% 0.44/0.66 (inj_0(s(z)) = inj_0(s(s(s(s(s(s(s(s(s(elem!1))))))))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[485])).
% 0.44/0.66 tff(487,plain,
% 0.44/0.66 (inj_0(s(s(s(s(s(s(s(s(s(elem!1)))))))))) = inj_0(s(z))),
% 0.44/0.66 inference(symmetry,[status(thm)],[486])).
% 0.44/0.66 tff(488,plain,
% 0.44/0.66 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(s(s(elem!1)))))))))) = s(s(s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(489,plain,
% 0.44/0.66 (inj_0(s(s(s(s(s(s(s(s(s(elem!1)))))))))) = s(s(s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[488, 22])).
% 0.44/0.66 tff(490,plain,
% 0.44/0.66 (s(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(s(s(s(s(elem!1))))))))))),
% 0.44/0.66 inference(symmetry,[status(thm)],[489])).
% 0.44/0.66 tff(491,plain,
% 0.44/0.66 (s(s(s(s(s(s(s(s(elem!1)))))))) = z),
% 0.44/0.66 inference(transitivity,[status(thm)],[490, 487, 24])).
% 0.44/0.66 tff(492,plain,
% 0.44/0.66 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(s(s(elem!1)))))))) = z))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(493,plain,
% 0.44/0.66 (~(s(s(s(s(s(s(s(s(elem!1)))))))) = z)),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[492, 46])).
% 0.44/0.66 tff(494,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[493, 491])).
% 0.44/0.66 tff(495,plain,((~(s(s(z)) = elem!1)) | (~(s(elem!1) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(496,plain,
% 0.44/0.66 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[495, 477])).
% 0.44/0.66 tff(497,plain,
% 0.44/0.66 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) <=> (s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.66 inference(commutativity,[status(thm)],[])).
% 0.44/0.66 tff(498,assumption,(s(s(s(s(s(s(elem!1)))))) = s(elem!1)), introduced(assumption)).
% 0.44/0.66 tff(499,plain,
% 0.44/0.66 (s(elem!1) = s(s(s(s(s(s(elem!1))))))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[498, 497])).
% 0.44/0.66 tff(500,assumption,(~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.44/0.66 tff(501,plain,
% 0.44/0.66 ($false),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[500, 499])).
% 0.44/0.66 tff(502,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.66 tff(503,plain,
% 0.44/0.66 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[502, 496])).
% 0.44/0.66 tff(504,assumption,(b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.44/0.66 tff(505,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(506,plain,
% 0.44/0.66 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.66 inference(rewrite,[status(thm)],[])).
% 0.44/0.66 tff(507,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.44/0.66 inference(monotonicity,[status(thm)],[506])).
% 0.44/0.66 tff(508,plain,
% 0.44/0.66 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.66 inference(transitivity,[status(thm)],[507, 505])).
% 0.44/0.66 tff(509,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.66 inference(quant_inst,[status(thm)],[])).
% 0.44/0.66 tff(510,plain,
% 0.44/0.66 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.44/0.66 inference(modus_ponens,[status(thm)],[509, 508])).
% 0.44/0.66 tff(511,plain,
% 0.44/0.66 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.66 inference(unit_resolution,[status(thm)],[510, 272, 253, 504])).
% 0.44/0.66 tff(512,assumption,(r(s(z), s(elem!1))), introduced(assumption)).
% 0.44/0.66 tff(513,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))), introduced(assumption)).
% 0.44/0.66 tff(514,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 0.44/0.67 tff(515,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(516,plain,
% 0.44/0.67 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(517,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[516])).
% 0.44/0.67 tff(518,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.67 inference(transitivity,[status(thm)],[517, 515])).
% 0.44/0.67 tff(519,plain,
% 0.44/0.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(520,plain,
% 0.44/0.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[519, 518])).
% 0.44/0.67 tff(521,plain,
% 0.44/0.67 ($false),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[520, 272, 291, 504, 514])).
% 0.44/0.67 tff(522,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.67 tff(523,plain,
% 0.44/0.67 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[522, 504, 291])).
% 0.44/0.67 tff(524,plain,
% 0.44/0.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(525,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(526,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[525, 524])).
% 0.44/0.67 tff(527,plain,
% 0.44/0.67 ((s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | b(s(s(s(s(s(s(elem!1)))))), s(elem!1)) | r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[526, 139])).
% 0.44/0.67 tff(528,plain,
% 0.44/0.67 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[527, 523, 513])).
% 0.44/0.67 tff(529,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(530,plain,
% 0.44/0.67 (((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(531,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[530])).
% 0.44/0.67 tff(532,plain,
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% 0.44/0.67 inference(transitivity,[status(thm)],[531, 529])).
% 0.44/0.67 tff(533,plain,
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% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(534,plain,
% 0.44/0.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[533, 532])).
% 0.44/0.67 tff(535,plain,
% 0.44/0.67 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[534, 371, 528, 512])).
% 0.44/0.67 tff(536,plain,
% 0.44/0.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(537,plain,
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% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(538,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(elem!1))))))) | b(s(z), s(s(s(s(s(s(elem!1))))))) | r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[537, 536])).
% 0.44/0.67 tff(539,plain,
% 0.44/0.67 ($false),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[538, 139, 155, 535, 511])).
% 0.44/0.67 tff(540,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(elem!1))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.67 tff(541,plain,
% 0.44/0.67 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[540, 503, 253, 307, 291])).
% 0.44/0.67 tff(542,plain,
% 0.44/0.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(543,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(544,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[543, 542])).
% 0.44/0.67 tff(545,plain,
% 0.44/0.67 ((s(s(s(s(s(s(elem!1)))))) = elem!1) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[544, 139])).
% 0.44/0.67 tff(546,plain,
% 0.44/0.67 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[545, 541, 221])).
% 0.44/0.67 tff(547,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
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% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(549,plain,
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% 0.44/0.67 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.44/0.67 tff(550,plain,
% 0.44/0.67 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[549, 371, 254, 546])).
% 0.44/0.67 tff(551,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))), introduced(assumption)).
% 0.44/0.67 tff(552,assumption,(r(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.44/0.67 tff(553,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(554,plain,
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% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(555,plain,
% 0.44/0.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[554, 553])).
% 0.44/0.67 tff(556,plain,
% 0.44/0.67 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[555, 371, 443, 552])).
% 0.44/0.67 tff(557,plain,
% 0.44/0.67 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(s(s(elem!1)))))) = z))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(558,plain,
% 0.44/0.67 (~(s(s(s(s(s(s(elem!1)))))) = z)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[557, 46])).
% 0.44/0.67 tff(559,plain,
% 0.44/0.67 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(560,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(561,plain,
% 0.44/0.67 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = z) | b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[560, 559])).
% 0.44/0.67 tff(562,plain,
% 0.44/0.67 (b(s(s(s(s(s(s(elem!1)))))), z) | r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[561, 139, 558])).
% 0.44/0.67 tff(563,plain,
% 0.44/0.67 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[562, 556])).
% 0.44/0.67 tff(564,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(565,plain,
% 0.44/0.67 (((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1))))) <=> ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(566,plain,
% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[565])).
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% 0.44/0.67 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.67 inference(transitivity,[status(thm)],[566, 564])).
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% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(569,plain,
% 0.44/0.67 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[568, 567])).
% 0.44/0.67 tff(570,plain,
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% 0.44/0.67 inference(unit_resolution,[status(thm)],[569, 371, 443, 254])).
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% 0.44/0.67 ((z = s(s(elem!1))) <=> (s(s(elem!1)) = z)),
% 0.44/0.67 inference(commutativity,[status(thm)],[])).
% 0.44/0.67 tff(572,plain,
% 0.44/0.67 ((s(s(elem!1)) = z) <=> (z = s(s(elem!1)))),
% 0.44/0.67 inference(symmetry,[status(thm)],[571])).
% 0.44/0.67 tff(573,plain,
% 0.44/0.67 ((~(s(s(elem!1)) = z)) <=> (~(z = s(s(elem!1))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[572])).
% 0.44/0.67 tff(574,plain,
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% 0.44/0.67 inference(modus_ponens,[status(thm)],[449, 573])).
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% 0.44/0.67 (((~![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))))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(576,plain,
% 0.44/0.67 ((~![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))))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(577,plain,
% 0.44/0.67 ((~![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)))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[576, 575])).
% 0.44/0.67 tff(578,plain,
% 0.44/0.67 ((z = s(s(elem!1))) | b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[577, 139])).
% 0.44/0.67 tff(579,plain,
% 0.44/0.67 (b(z, s(s(elem!1))) | r(z, s(s(elem!1)))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[578, 574])).
% 0.44/0.67 tff(580,plain,
% 0.44/0.67 (b(z, s(s(elem!1)))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[579, 570])).
% 0.44/0.67 tff(581,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(582,plain,
% 0.44/0.67 (((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.67 inference(rewrite,[status(thm)],[])).
% 0.44/0.67 tff(583,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[582])).
% 0.44/0.67 tff(584,plain,
% 0.44/0.67 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.67 inference(transitivity,[status(thm)],[583, 581])).
% 0.44/0.67 tff(585,plain,
% 0.44/0.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(586,plain,
% 0.44/0.67 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.44/0.67 inference(modus_ponens,[status(thm)],[585, 584])).
% 0.44/0.67 tff(587,plain,
% 0.44/0.67 ($false),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[586, 272, 580, 563, 551])).
% 0.44/0.67 tff(588,plain,((~r(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.67 tff(589,plain,
% 0.44/0.67 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[588, 546, 433, 254])).
% 0.44/0.67 tff(590,plain,
% 0.44/0.67 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[175])).
% 0.44/0.67 tff(591,plain,
% 0.44/0.67 (s(s(s(s(s(elem!1))))) = s(elem!1)),
% 0.44/0.67 inference(transitivity,[status(thm)],[33, 590, 27])).
% 0.44/0.67 tff(592,plain,
% 0.44/0.67 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(elem!1))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[591])).
% 0.44/0.67 tff(593,plain,
% 0.44/0.67 (inj_0(s(elem!1)) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.44/0.67 inference(symmetry,[status(thm)],[592])).
% 0.44/0.67 tff(594,plain,
% 0.44/0.67 (s(s(z)) = s(s(s(s(elem!1))))),
% 0.44/0.67 inference(transitivity,[status(thm)],[204, 89, 593, 37])).
% 0.44/0.67 tff(595,plain,
% 0.44/0.67 (inj_0(s(s(z))) = inj_0(s(s(s(s(elem!1)))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[594])).
% 0.44/0.67 tff(596,plain,
% 0.44/0.67 (s(z) = s(s(s(elem!1)))),
% 0.44/0.67 inference(transitivity,[status(thm)],[213, 595, 164])).
% 0.44/0.67 tff(597,assumption,(s(z) = s(s(s(elem!1)))), introduced(assumption)).
% 0.44/0.67 tff(598,plain,
% 0.44/0.67 (inj_0(s(z)) = inj_0(s(s(s(elem!1))))),
% 0.44/0.67 inference(monotonicity,[status(thm)],[597])).
% 0.44/0.67 tff(599,plain,
% 0.44/0.67 (inj_0(s(s(s(elem!1)))) = inj_0(s(z))),
% 0.44/0.67 inference(symmetry,[status(thm)],[598])).
% 0.44/0.67 tff(600,plain,
% 0.44/0.67 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(elem!1)))) = s(s(elem!1)))),
% 0.44/0.67 inference(quant_inst,[status(thm)],[])).
% 0.44/0.67 tff(601,plain,
% 0.44/0.67 (inj_0(s(s(s(elem!1)))) = s(s(elem!1))),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[600, 22])).
% 0.44/0.67 tff(602,plain,
% 0.44/0.67 (s(s(elem!1)) = inj_0(s(s(s(elem!1))))),
% 0.44/0.67 inference(symmetry,[status(thm)],[601])).
% 0.44/0.67 tff(603,plain,
% 0.44/0.67 (s(s(elem!1)) = z),
% 0.44/0.67 inference(transitivity,[status(thm)],[602, 599, 24])).
% 0.44/0.67 tff(604,plain,
% 0.44/0.67 ($false),
% 0.44/0.67 inference(unit_resolution,[status(thm)],[449, 603])).
% 0.44/0.67 tff(605,plain,(~(s(z) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(606,plain,
% 0.44/0.68 ($false),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[605, 596])).
% 0.44/0.68 tff(607,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) | (~(s(s(z)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(608,plain,
% 0.44/0.68 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[607, 477])).
% 0.44/0.68 tff(609,plain,
% 0.44/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(610,plain,
% 0.44/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(611,plain,
% 0.44/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))) | r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[610, 609])).
% 0.44/0.68 tff(612,plain,
% 0.44/0.68 ($false),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[611, 139, 608, 589, 550])).
% 0.44/0.68 tff(613,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(s(z), elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(614,plain,
% 0.44/0.68 (~b(s(elem!1), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[613, 254, 221, 253, 203, 248])).
% 0.44/0.68 tff(615,plain,
% 0.44/0.68 (((~![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))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(616,plain,
% 0.44/0.68 ((~![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))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(617,plain,
% 0.44/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[616, 615])).
% 0.44/0.68 tff(618,plain,
% 0.44/0.68 ((s(elem!1) = elem!1) | b(s(elem!1), elem!1) | r(s(elem!1), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[617, 139])).
% 0.44/0.68 tff(619,plain,
% 0.44/0.68 (r(s(elem!1), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[618, 614, 247])).
% 0.44/0.68 tff(620,assumption,(s(elem!1) = s(s(elem!1))), introduced(assumption)).
% 0.44/0.68 tff(621,plain,
% 0.44/0.68 (s(s(elem!1)) = s(elem!1)),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[620, 59])).
% 0.44/0.68 tff(622,plain,
% 0.44/0.68 ($false),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[244, 621])).
% 0.44/0.68 tff(623,plain,((~(s(elem!1) = s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(624,plain,
% 0.44/0.68 (~(s(elem!1) = s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[623, 237])).
% 0.44/0.68 tff(625,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(626,plain,
% 0.44/0.68 (((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(627,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))))),
% 0.44/0.68 inference(monotonicity,[status(thm)],[626])).
% 0.44/0.68 tff(628,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)))),
% 0.44/0.68 inference(transitivity,[status(thm)],[627, 625])).
% 0.44/0.68 tff(629,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1)))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(630,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[629, 628])).
% 0.44/0.68 tff(631,plain,
% 0.44/0.68 (~r(s(elem!1), s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[630, 371, 254, 619])).
% 0.44/0.68 tff(632,plain,
% 0.44/0.68 (((~![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))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(633,plain,
% 0.44/0.68 ((~![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))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(634,plain,
% 0.44/0.68 ((~![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)))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[633, 632])).
% 0.44/0.68 tff(635,plain,
% 0.44/0.68 ((s(elem!1) = s(s(elem!1))) | b(s(elem!1), s(s(elem!1))) | r(s(elem!1), s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[634, 139])).
% 0.44/0.68 tff(636,plain,
% 0.44/0.68 (b(s(elem!1), s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[635, 631, 624])).
% 0.44/0.68 tff(637,assumption,(r(s(elem!1), elem!1)), introduced(assumption)).
% 0.44/0.68 tff(638,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(639,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z)))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(640,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(z))))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[639, 638])).
% 0.44/0.68 tff(641,plain,
% 0.44/0.68 (~r(s(elem!1), s(s(z)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[640, 371, 434, 637])).
% 0.44/0.68 tff(642,plain,
% 0.44/0.68 (b(s(elem!1), s(s(z)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[336, 139, 248, 641])).
% 0.44/0.68 tff(643,assumption,(b(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.44/0.68 tff(644,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(645,plain,
% 0.44/0.68 (((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(646,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.44/0.68 inference(monotonicity,[status(thm)],[645])).
% 0.44/0.68 tff(647,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.44/0.68 inference(transitivity,[status(thm)],[646, 644])).
% 0.44/0.68 tff(648,plain,
% 0.44/0.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(elem!1), s(s(z)))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(649,plain,
% 0.44/0.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1))))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[648, 647])).
% 0.44/0.68 tff(650,plain,
% 0.44/0.68 ($false),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[649, 272, 643, 442, 642])).
% 0.44/0.68 tff(651,plain,((~r(s(s(z)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (s(s(z)) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(652,plain,
% 0.44/0.68 (~r(s(s(z)), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[651, 636, 248, 203, 619, 254])).
% 0.44/0.68 tff(653,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(654,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(655,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[654, 653])).
% 0.44/0.68 tff(656,plain,
% 0.44/0.68 (~r(s(s(elem!1)), s(elem!1))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[655, 371, 254, 619])).
% 0.44/0.68 tff(657,plain,
% 0.44/0.68 (((~![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)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(658,plain,
% 0.44/0.68 ((~![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)))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(659,plain,
% 0.44/0.68 ((~![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))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[658, 657])).
% 0.44/0.68 tff(660,plain,
% 0.44/0.68 ((s(s(elem!1)) = s(elem!1)) | b(s(s(elem!1)), s(elem!1)) | r(s(s(elem!1)), s(elem!1))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[659, 139])).
% 0.44/0.68 tff(661,plain,
% 0.44/0.68 (b(s(s(elem!1)), s(elem!1))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[660, 656, 237])).
% 0.44/0.68 tff(662,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), introduced(assumption)).
% 0.44/0.68 tff(663,plain,
% 0.44/0.68 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[538, 139, 155, 511])).
% 0.44/0.68 tff(664,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(665,plain,
% 0.44/0.68 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(666,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.44/0.68 inference(monotonicity,[status(thm)],[665])).
% 0.44/0.68 tff(667,plain,
% 0.44/0.68 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.44/0.68 inference(transitivity,[status(thm)],[666, 664])).
% 0.44/0.68 tff(668,plain,
% 0.44/0.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(669,plain,
% 0.44/0.68 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[668, 667])).
% 0.44/0.68 tff(670,plain,
% 0.44/0.68 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[669, 272, 262, 504])).
% 0.44/0.68 tff(671,plain,
% 0.44/0.68 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[562, 670])).
% 0.44/0.68 tff(672,assumption,(r(s(z), z)), introduced(assumption)).
% 0.44/0.68 tff(673,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(674,plain,
% 0.44/0.68 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(675,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.44/0.68 inference(monotonicity,[status(thm)],[674])).
% 0.44/0.68 tff(676,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.44/0.68 inference(transitivity,[status(thm)],[675, 673])).
% 0.44/0.68 tff(677,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(678,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[677, 676])).
% 0.44/0.68 tff(679,plain,
% 0.44/0.68 ($false),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[678, 371, 672, 671, 663])).
% 0.44/0.68 tff(680,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.68 tff(681,plain,
% 0.44/0.68 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[680, 290, 253, 262])).
% 0.44/0.68 tff(682,plain,
% 0.44/0.68 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[545, 681, 221])).
% 0.44/0.68 tff(683,plain,
% 0.44/0.68 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[549, 371, 254, 552])).
% 0.44/0.68 tff(684,plain,
% 0.44/0.68 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[611, 139, 662, 683])).
% 0.44/0.68 tff(685,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(686,plain,
% 0.44/0.68 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(687,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))))),
% 0.44/0.68 inference(monotonicity,[status(thm)],[686])).
% 0.44/0.68 tff(688,plain,
% 0.44/0.68 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.68 inference(transitivity,[status(thm)],[687, 685])).
% 0.44/0.68 tff(689,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(690,plain,
% 0.44/0.68 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[689, 688])).
% 0.44/0.68 tff(691,plain,
% 0.44/0.68 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.68 inference(unit_resolution,[status(thm)],[690, 371, 637, 552])).
% 0.44/0.68 tff(692,plain,
% 0.44/0.68 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.68 inference(rewrite,[status(thm)],[])).
% 0.44/0.68 tff(693,plain,
% 0.44/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1))))))))),
% 0.44/0.68 inference(quant_inst,[status(thm)],[])).
% 0.44/0.68 tff(694,plain,
% 0.44/0.68 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | b(s(elem!1), s(s(s(s(s(s(elem!1))))))) | r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.44/0.68 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.44/0.68 tff(695,plain,
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% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(756,plain,
% 0.44/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))))),
% 0.44/0.69 inference(monotonicity,[status(thm)],[755])).
% 0.44/0.69 tff(757,plain,
% 0.44/0.69 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(transitivity,[status(thm)],[756, 754])).
% 0.44/0.69 tff(758,plain,
% 0.44/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(759,plain,
% 0.44/0.69 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[758, 757])).
% 0.44/0.69 tff(760,plain,
% 0.44/0.69 ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(elem!1))))))) | (~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[759, 371])).
% 0.44/0.69 tff(761,plain,
% 0.44/0.69 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[760, 753, 727])).
% 0.44/0.69 tff(762,plain,
% 0.44/0.69 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(763,plain,
% 0.44/0.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(764,plain,
% 0.44/0.69 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[763, 762])).
% 0.44/0.69 tff(765,plain,
% 0.44/0.69 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(z))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[764, 139, 761])).
% 0.44/0.69 tff(766,plain,
% 0.44/0.69 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[765, 749])).
% 0.44/0.69 tff(767,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.44/0.69 tff(768,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(769,plain,
% 0.44/0.69 (((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))) <=> ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(770,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))))),
% 0.44/0.69 inference(monotonicity,[status(thm)],[769])).
% 0.44/0.69 tff(771,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(transitivity,[status(thm)],[770, 768])).
% 0.44/0.69 tff(772,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(773,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[772, 771])).
% 0.44/0.69 tff(774,plain,
% 0.44/0.69 ($false),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[773, 272, 767, 766, 742])).
% 0.44/0.69 tff(775,plain,((~r(s(s(z)), s(s(s(s(s(elem!1))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(z)) = s(s(elem!1))) | (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))) | (s(elem!1) = s(s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.69 tff(776,plain,
% 0.44/0.69 (~r(s(s(z)), s(s(s(s(s(elem!1))))))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[775, 719, 203, 705, 248, 714, 682])).
% 0.44/0.69 tff(777,plain,
% 0.44/0.69 (~r(s(s(z)), elem!1)),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[776, 711])).
% 0.44/0.69 tff(778,plain,
% 0.44/0.69 (b(s(s(z)), elem!1)),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[476, 777, 706])).
% 0.44/0.69 tff(779,assumption,(b(s(s(z)), z)), introduced(assumption)).
% 0.44/0.69 tff(780,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(781,plain,
% 0.44/0.69 (((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(782,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))))),
% 0.44/0.69 inference(monotonicity,[status(thm)],[781])).
% 0.44/0.69 tff(783,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)))),
% 0.44/0.69 inference(transitivity,[status(thm)],[782, 780])).
% 0.44/0.69 tff(784,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), z)))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(785,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(z, elem!1))),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[784, 783])).
% 0.44/0.69 tff(786,plain,
% 0.44/0.69 ($false),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[785, 272, 262, 326, 779])).
% 0.44/0.69 tff(787,plain,((~b(z, elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.69 tff(788,plain,
% 0.44/0.69 (~b(s(s(z)), z)),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[787, 778, 262])).
% 0.44/0.69 tff(789,plain,
% 0.44/0.69 (r(s(s(z)), z)),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[462, 788])).
% 0.44/0.69 tff(790,assumption,(b(s(z), s(s(z)))), introduced(assumption)).
% 0.44/0.69 tff(791,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(792,plain,
% 0.44/0.69 (((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(793,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))))),
% 0.44/0.69 inference(monotonicity,[status(thm)],[792])).
% 0.44/0.69 tff(794,plain,
% 0.44/0.69 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)))),
% 0.44/0.69 inference(transitivity,[status(thm)],[793, 791])).
% 0.44/0.69 tff(795,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(796,plain,
% 0.44/0.69 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))),
% 0.44/0.69 inference(modus_ponens,[status(thm)],[795, 794])).
% 0.44/0.69 tff(797,plain,
% 0.44/0.69 ($false),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[796, 272, 790, 326, 253])).
% 0.44/0.69 tff(798,plain,((~b(s(s(z)), elem!1)) | (~b(s(z), s(s(z)))) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.44/0.69 tff(799,plain,
% 0.44/0.69 (~b(s(z), s(s(z)))),
% 0.44/0.69 inference(unit_resolution,[status(thm)],[798, 778, 253])).
% 0.44/0.69 tff(800,plain,
% 0.44/0.69 (((~![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))))),
% 0.44/0.69 inference(rewrite,[status(thm)],[])).
% 0.44/0.69 tff(801,plain,
% 0.44/0.69 ((~![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))))),
% 0.44/0.69 inference(quant_inst,[status(thm)],[])).
% 0.44/0.69 tff(802,plain,
% 0.44/0.69 ((~![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)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[801, 800])).
% 0.51/0.70 tff(803,plain,
% 0.51/0.70 ((s(z) = s(s(z))) | b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[802, 139])).
% 0.51/0.70 tff(804,plain,
% 0.51/0.70 (b(s(z), s(s(z))) | r(s(z), s(s(z)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[803, 353])).
% 0.51/0.70 tff(805,plain,
% 0.51/0.70 (r(s(z), s(s(z)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[804, 799])).
% 0.51/0.70 tff(806,plain,
% 0.51/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(807,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z)))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(808,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(z))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.51/0.70 tff(809,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[808, 371, 805, 789, 290])).
% 0.51/0.70 tff(810,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(z))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(811,plain,
% 0.51/0.70 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[810, 262, 203, 248, 253, 254, 619, 636, 661, 221])).
% 0.51/0.70 tff(812,plain,
% 0.51/0.70 (~(s(s(z)) = elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[607, 811])).
% 0.51/0.70 tff(813,plain,
% 0.51/0.70 (b(s(s(z)), elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[476, 812, 652])).
% 0.51/0.70 tff(814,plain,
% 0.51/0.70 (~b(s(s(z)), z)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[787, 813, 262])).
% 0.51/0.70 tff(815,plain,
% 0.51/0.70 (r(s(s(z)), z)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[462, 814])).
% 0.51/0.70 tff(816,plain,
% 0.51/0.70 (~b(s(z), s(s(z)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[798, 813, 253])).
% 0.51/0.70 tff(817,plain,
% 0.51/0.70 (r(s(z), s(s(z)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[804, 816])).
% 0.51/0.70 tff(818,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[808, 371, 817, 815, 290])).
% 0.51/0.70 tff(819,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(z))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(820,plain,
% 0.51/0.70 (~b(z, elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[819, 254, 203, 248, 253, 221])).
% 0.51/0.70 tff(821,plain,
% 0.51/0.70 (r(z, elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[432, 820, 261])).
% 0.51/0.70 tff(822,plain,
% 0.51/0.70 (~r(z, s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[569, 371, 821, 254])).
% 0.51/0.70 tff(823,plain,
% 0.51/0.70 (b(z, s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[579, 822])).
% 0.51/0.70 tff(824,plain,
% 0.51/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(825,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(826,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[825, 824])).
% 0.51/0.70 tff(827,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[826, 371, 443, 416, 637])).
% 0.51/0.70 tff(828,plain,((~r(z, elem!1)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(829,plain,
% 0.51/0.70 (~r(s(elem!1), z)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[828, 821, 619])).
% 0.51/0.70 tff(830,plain,
% 0.51/0.70 (b(s(elem!1), z)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[414, 829])).
% 0.51/0.70 tff(831,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(832,plain,
% 0.51/0.70 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(833,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[832])).
% 0.51/0.70 tff(834,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[833, 831])).
% 0.51/0.70 tff(835,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(836,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[835, 834])).
% 0.51/0.70 tff(837,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[836, 272, 830, 636, 823])).
% 0.51/0.70 tff(838,plain,((~r(s(s(elem!1)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(z))) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(839,plain,
% 0.51/0.70 (~r(s(s(elem!1)), elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[838, 253, 248, 203, 221])).
% 0.51/0.70 tff(840,plain,
% 0.51/0.70 (((~![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))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(841,plain,
% 0.51/0.70 ((~![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))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(842,plain,
% 0.51/0.70 ((~![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)),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[841, 840])).
% 0.51/0.70 tff(843,plain,
% 0.51/0.70 ((s(s(elem!1)) = elem!1) | b(s(s(elem!1)), elem!1) | r(s(s(elem!1)), elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[842, 139])).
% 0.51/0.70 tff(844,plain,
% 0.51/0.70 (b(s(s(elem!1)), elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[843, 839, 231])).
% 0.51/0.70 tff(845,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(846,plain,
% 0.51/0.70 (((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(847,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[846])).
% 0.51/0.70 tff(848,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[847, 845])).
% 0.51/0.70 tff(849,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(850,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), s(s(elem!1))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[849, 848])).
% 0.51/0.70 tff(851,plain,
% 0.51/0.70 (~b(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[850, 272, 253, 844])).
% 0.51/0.70 tff(852,assumption,(s(z) = s(s(elem!1))), introduced(assumption)).
% 0.51/0.70 tff(853,plain,
% 0.51/0.70 (inj_0(s(z)) = inj_0(s(s(elem!1)))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[852])).
% 0.51/0.70 tff(854,plain,
% 0.51/0.70 (inj_0(s(s(elem!1))) = inj_0(s(z))),
% 0.51/0.70 inference(symmetry,[status(thm)],[853])).
% 0.51/0.70 tff(855,plain,
% 0.51/0.70 (s(elem!1) = z),
% 0.51/0.70 inference(transitivity,[status(thm)],[68, 854, 24])).
% 0.51/0.70 tff(856,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[410, 855])).
% 0.51/0.70 tff(857,plain,(~(s(z) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(858,plain,
% 0.51/0.70 (((~![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))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(859,plain,
% 0.51/0.70 ((~![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))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(860,plain,
% 0.51/0.70 ((~![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)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[859, 858])).
% 0.51/0.70 tff(861,plain,
% 0.51/0.70 ((s(z) = s(s(elem!1))) | b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[860, 139])).
% 0.51/0.70 tff(862,plain,
% 0.51/0.70 (b(s(z), s(s(elem!1))) | r(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[861, 857])).
% 0.51/0.70 tff(863,plain,
% 0.51/0.70 (r(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[862, 851])).
% 0.51/0.70 tff(864,assumption,(b(s(s(elem!1)), elem!1)), introduced(assumption)).
% 0.51/0.70 tff(865,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(866,plain,
% 0.51/0.70 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(867,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[866])).
% 0.51/0.70 tff(868,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[867, 865])).
% 0.51/0.70 tff(869,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(870,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(z)), s(s(elem!1))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[869, 868])).
% 0.51/0.70 tff(871,plain,
% 0.51/0.70 (~b(s(s(z)), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[870, 272, 326, 864])).
% 0.51/0.70 tff(872,plain,
% 0.51/0.70 (r(s(s(z)), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[441, 139, 203, 871])).
% 0.51/0.70 tff(873,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(874,plain,
% 0.51/0.70 (((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(875,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))))),
% 0.51/0.70 inference(monotonicity,[status(thm)],[874])).
% 0.51/0.70 tff(876,plain,
% 0.51/0.70 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.70 inference(transitivity,[status(thm)],[875, 873])).
% 0.51/0.70 tff(877,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(878,plain,
% 0.51/0.70 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(z)))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[877, 876])).
% 0.51/0.70 tff(879,plain,
% 0.51/0.70 (~b(s(s(elem!1)), s(z))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[878, 272, 253, 864])).
% 0.51/0.70 tff(880,assumption,(~r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.51/0.70 tff(881,assumption,(s(s(elem!1)) = s(z)), introduced(assumption)).
% 0.51/0.70 tff(882,plain,
% 0.51/0.70 (s(z) = s(s(elem!1))),
% 0.51/0.70 inference(symmetry,[status(thm)],[881])).
% 0.51/0.70 tff(883,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[857, 882])).
% 0.51/0.70 tff(884,plain,(~(s(s(elem!1)) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(885,assumption,(~b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.51/0.70 tff(886,plain,
% 0.51/0.70 (((~![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)))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(887,plain,
% 0.51/0.70 ((~![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)))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(888,plain,
% 0.51/0.70 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(z)) | b(s(s(elem!1)), s(z)) | r(s(s(elem!1)), s(z))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[887, 886])).
% 0.51/0.70 tff(889,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[888, 139, 885, 884, 880])).
% 0.51/0.70 tff(890,plain,(r(s(s(elem!1)), s(z)) | b(s(s(elem!1)), s(z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(891,plain,
% 0.51/0.70 (r(s(s(elem!1)), s(z))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[890, 879])).
% 0.51/0.70 tff(892,plain,
% 0.51/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(893,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.51/0.70 inference(quant_inst,[status(thm)],[])).
% 0.51/0.70 tff(894,plain,
% 0.51/0.70 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(elem!1))))),
% 0.51/0.70 inference(modus_ponens,[status(thm)],[893, 892])).
% 0.51/0.70 tff(895,plain,
% 0.51/0.70 ($false),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[894, 371, 891, 360, 872])).
% 0.51/0.70 tff(896,plain,((~b(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.70 tff(897,plain,
% 0.51/0.70 (~b(s(s(z)), elem!1)),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[896, 844, 253, 203])).
% 0.51/0.70 tff(898,assumption,(~(s(elem!1) = s(s(elem!1)))), introduced(assumption)).
% 0.51/0.70 tff(899,plain,
% 0.51/0.70 (~b(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[850, 272, 253, 864])).
% 0.51/0.70 tff(900,plain,
% 0.51/0.70 (r(s(z), s(s(elem!1)))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[862, 899])).
% 0.51/0.70 tff(901,plain,
% 0.51/0.70 (r(s(elem!1), s(z))),
% 0.51/0.70 inference(unit_resolution,[status(thm)],[324, 317, 11])).
% 0.51/0.70 tff(902,assumption,(r(s(elem!1), s(s(elem!1)))), introduced(assumption)).
% 0.51/0.70 tff(903,assumption,(r(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.51/0.70 tff(904,plain,
% 0.51/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(905,plain,
% 0.51/0.70 (((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z)))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.70 inference(rewrite,[status(thm)],[])).
% 0.51/0.70 tff(906,plain,
% 0.51/0.70 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[905])).
% 0.51/0.71 tff(907,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.71 inference(transitivity,[status(thm)],[906, 904])).
% 0.51/0.71 tff(908,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(909,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(z))) | (~r(s(z), s(s(elem!1))))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[908, 907])).
% 0.51/0.71 tff(910,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[909, 371, 903, 902, 361])).
% 0.51/0.71 tff(911,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(912,plain,
% 0.51/0.71 (~r(s(elem!1), s(s(elem!1)))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[911, 901, 900])).
% 0.51/0.71 tff(913,plain,
% 0.51/0.71 (b(s(elem!1), s(s(elem!1)))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[635, 912, 898])).
% 0.51/0.71 tff(914,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), 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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(915,plain,
% 0.51/0.71 (((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(916,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[915])).
% 0.51/0.71 tff(917,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[916, 914])).
% 0.51/0.71 tff(918,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(919,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[918, 917])).
% 0.51/0.71 tff(920,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[919, 272, 864, 291, 913])).
% 0.51/0.71 tff(921,plain,((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = s(z)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(922,plain,
% 0.51/0.71 (~b(s(elem!1), elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[921, 844, 624, 259, 253])).
% 0.51/0.71 tff(923,plain,
% 0.51/0.71 (r(s(elem!1), elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[618, 922, 247])).
% 0.51/0.71 tff(924,plain,
% 0.51/0.71 (~r(s(elem!1), z)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[828, 443, 637])).
% 0.51/0.71 tff(925,plain,
% 0.51/0.71 (b(s(elem!1), z)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[414, 924])).
% 0.51/0.71 tff(926,plain,
% 0.51/0.71 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.71 inference(symmetry,[status(thm)],[174])).
% 0.51/0.71 tff(927,plain,
% 0.51/0.71 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[495, 204])).
% 0.51/0.71 tff(928,plain,
% 0.51/0.71 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[694, 139, 500, 691])).
% 0.51/0.71 tff(929,plain,
% 0.51/0.71 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[561, 139, 558, 556])).
% 0.51/0.71 tff(930,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(931,plain,
% 0.51/0.71 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(932,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[931])).
% 0.51/0.71 tff(933,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[932, 930])).
% 0.51/0.71 tff(934,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(935,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[934, 933])).
% 0.51/0.71 tff(936,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[935, 272, 399, 929, 928])).
% 0.51/0.71 tff(937,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(938,plain,
% 0.51/0.71 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[937, 927, 637, 443, 925])).
% 0.51/0.71 tff(939,plain,
% 0.51/0.71 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[545, 938, 221])).
% 0.51/0.71 tff(940,plain,
% 0.51/0.71 (~b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[510, 272, 253, 939])).
% 0.51/0.71 tff(941,plain,
% 0.51/0.71 (r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[538, 139, 155, 940])).
% 0.51/0.71 tff(942,assumption,(r(s(z), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.51/0.71 tff(943,assumption,(r(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.51/0.71 tff(944,assumption,(r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.51/0.71 tff(945,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(946,plain,
% 0.51/0.71 (((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(947,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[946])).
% 0.51/0.71 tff(948,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(transitivity,[status(thm)],[947, 945])).
% 0.51/0.71 tff(949,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(950,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[949, 948])).
% 0.51/0.71 tff(951,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[950, 371, 944, 943, 942])).
% 0.51/0.71 tff(952,plain,((~r(s(z), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(953,plain,
% 0.51/0.71 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[952, 941, 891])).
% 0.51/0.71 tff(954,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(955,plain,
% 0.51/0.71 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(956,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[955])).
% 0.51/0.71 tff(957,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(transitivity,[status(thm)],[956, 954])).
% 0.51/0.71 tff(958,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(959,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[958, 957])).
% 0.51/0.71 tff(960,plain,
% 0.51/0.71 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[959, 272, 864, 939])).
% 0.51/0.71 tff(961,plain,
% 0.51/0.71 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(962,plain,
% 0.51/0.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(963,plain,
% 0.51/0.71 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[962, 961])).
% 0.51/0.71 tff(964,plain,
% 0.51/0.71 ((s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[963, 139, 960])).
% 0.51/0.71 tff(965,plain,
% 0.51/0.71 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[964, 953])).
% 0.51/0.71 tff(966,plain,
% 0.51/0.71 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[965, 926])).
% 0.51/0.71 tff(967,plain,
% 0.51/0.71 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[607, 204])).
% 0.51/0.71 tff(968,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[967, 966])).
% 0.51/0.71 tff(969,plain,((~(s(s(z)) = elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(elem!1), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(970,plain,
% 0.51/0.71 (~(s(s(z)) = elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[969, 443, 253, 221, 637, 864])).
% 0.51/0.71 tff(971,plain,
% 0.51/0.71 (r(s(s(z)), elem!1)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[476, 970, 202])).
% 0.51/0.71 tff(972,assumption,(r(elem!1, z)), introduced(assumption)).
% 0.51/0.71 tff(973,assumption,(r(s(s(z)), z)), introduced(assumption)).
% 0.51/0.71 tff(974,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(975,plain,
% 0.51/0.71 (((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(976,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[975])).
% 0.51/0.71 tff(977,plain,
% 0.51/0.71 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[976, 974])).
% 0.51/0.71 tff(978,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), elem!1)))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(979,plain,
% 0.51/0.71 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(elem!1, z)) | (~r(s(s(z)), elem!1))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[978, 977])).
% 0.51/0.71 tff(980,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[979, 371, 972, 434, 973])).
% 0.51/0.71 tff(981,plain,((~r(elem!1, z)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(982,plain,
% 0.51/0.71 (~r(s(s(z)), z)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[981, 434, 972])).
% 0.51/0.71 tff(983,plain,
% 0.51/0.71 (b(s(s(z)), z)),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[462, 982])).
% 0.51/0.71 tff(984,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(985,plain,
% 0.51/0.71 (((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))),
% 0.51/0.71 inference(rewrite,[status(thm)],[])).
% 0.51/0.71 tff(986,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z))))),
% 0.51/0.71 inference(monotonicity,[status(thm)],[985])).
% 0.51/0.71 tff(987,plain,
% 0.51/0.71 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z)))),
% 0.51/0.71 inference(transitivity,[status(thm)],[986, 984])).
% 0.51/0.71 tff(988,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(elem!1), z)) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))))),
% 0.51/0.71 inference(quant_inst,[status(thm)],[])).
% 0.51/0.71 tff(989,plain,
% 0.51/0.71 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), z))),
% 0.51/0.71 inference(modus_ponens,[status(thm)],[988, 987])).
% 0.51/0.71 tff(990,plain,
% 0.51/0.71 (~b(s(elem!1), s(s(z)))),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[989, 272, 983, 399])).
% 0.51/0.71 tff(991,plain,
% 0.51/0.71 ($false),
% 0.51/0.71 inference(unit_resolution,[status(thm)],[336, 139, 248, 990, 641])).
% 0.51/0.71 tff(992,plain,((~r(s(s(z)), elem!1)) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.71 tff(993,plain,
% 0.51/0.71 (~r(elem!1, z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[992, 971, 248, 637, 925])).
% 0.51/0.72 tff(994,plain,
% 0.51/0.72 (((~![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))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(995,plain,
% 0.51/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = z) | b(elem!1, z) | r(elem!1, z))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(996,plain,
% 0.51/0.72 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[995, 994])).
% 0.51/0.72 tff(997,plain,
% 0.51/0.72 ((elem!1 = z) | b(elem!1, z) | r(elem!1, z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[996, 139])).
% 0.51/0.72 tff(998,plain,
% 0.51/0.72 (b(elem!1, z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[997, 993, 5])).
% 0.51/0.72 tff(999,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1000,plain,
% 0.51/0.72 (((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))) <=> ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1001,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1000])).
% 0.51/0.72 tff(1002,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1001, 999])).
% 0.51/0.72 tff(1003,plain,
% 0.51/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1004,plain,
% 0.51/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1003, 1002])).
% 0.51/0.72 tff(1005,plain,
% 0.51/0.72 ((~b(s(z), z)) | (~b(elem!1, z)) | (~b(s(z), elem!1))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1004, 272])).
% 0.51/0.72 tff(1006,plain,
% 0.51/0.72 (~b(s(z), z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1005, 998, 253])).
% 0.51/0.72 tff(1007,plain,
% 0.51/0.72 (r(s(z), z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[289, 1006])).
% 0.51/0.72 tff(1008,assumption,(r(z, s(s(elem!1)))), introduced(assumption)).
% 0.51/0.72 tff(1009,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1010,plain,
% 0.51/0.72 (((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1011,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1010])).
% 0.51/0.72 tff(1012,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1011, 1009])).
% 0.51/0.72 tff(1013,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1014,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1))))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1013, 1012])).
% 0.51/0.72 tff(1015,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1014, 371, 903, 672, 1008])).
% 0.51/0.72 tff(1016,plain,((~r(z, s(s(elem!1)))) | (~r(s(z), s(s(elem!1)))) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(1017,plain,
% 0.51/0.72 (~r(z, s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1016, 1007, 900])).
% 0.51/0.72 tff(1018,plain,
% 0.51/0.72 (b(z, s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[579, 1017])).
% 0.51/0.72 tff(1019,assumption,(r(s(s(elem!1)), z)), introduced(assumption)).
% 0.51/0.72 tff(1020,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1021,plain,
% 0.51/0.72 (((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1022,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1021])).
% 0.51/0.72 tff(1023,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1022, 1020])).
% 0.51/0.72 tff(1024,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(z), z)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1025,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1024, 1023])).
% 0.51/0.72 tff(1026,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1025, 371, 1019, 903, 672])).
% 0.51/0.72 tff(1027,plain,((~r(s(z), z)) | (~r(s(s(elem!1)), z)) | (~r(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(1028,plain,
% 0.51/0.72 (~r(s(s(elem!1)), z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1027, 1007, 900])).
% 0.51/0.72 tff(1029,plain,
% 0.51/0.72 (b(s(s(elem!1)), z)),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[453, 1028])).
% 0.51/0.72 tff(1030,assumption,(b(s(s(elem!1)), z)), introduced(assumption)).
% 0.51/0.72 tff(1031,assumption,(b(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.51/0.72 tff(1032,assumption,(b(elem!1, z)), introduced(assumption)).
% 0.51/0.72 tff(1033,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1034,plain,
% 0.51/0.72 (((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(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)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1035,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1034])).
% 0.51/0.72 tff(1036,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1035, 1033])).
% 0.51/0.72 tff(1037,plain,
% 0.51/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(elem!1, z)) | (~b(s(s(elem!1)), z)) | (~b(elem!1, s(s(elem!1)))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1038,plain,
% 0.51/0.72 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1037, 1036])).
% 0.51/0.72 tff(1039,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1038, 272, 1032, 1031, 1030])).
% 0.51/0.72 tff(1040,plain,((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(1041,plain,
% 0.51/0.72 (~b(elem!1, s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1040, 1029, 998])).
% 0.51/0.72 tff(1042,plain,
% 0.51/0.72 (((~![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))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1043,plain,
% 0.51/0.72 ((~![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))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1044,plain,
% 0.51/0.72 ((~![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)))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1043, 1042])).
% 0.51/0.72 tff(1045,plain,
% 0.51/0.72 ((elem!1 = s(s(elem!1))) | b(elem!1, s(s(elem!1))) | r(elem!1, s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1044, 139])).
% 0.51/0.72 tff(1046,plain,
% 0.51/0.72 (r(elem!1, s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1045, 1041, 236])).
% 0.51/0.72 tff(1047,assumption,(r(elem!1, s(s(elem!1)))), introduced(assumption)).
% 0.51/0.72 tff(1048,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1049,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1050,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1049, 1048])).
% 0.51/0.72 tff(1051,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1050, 371, 1047, 637, 902])).
% 0.51/0.72 tff(1052,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(1053,plain,
% 0.51/0.72 (~r(s(elem!1), s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1052, 1046, 637])).
% 0.51/0.72 tff(1054,plain,
% 0.51/0.72 (b(s(elem!1), s(s(elem!1)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[635, 1053, 624])).
% 0.51/0.72 tff(1055,assumption,(r(z, s(s(z)))), introduced(assumption)).
% 0.51/0.72 tff(1056,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1057,plain,
% 0.51/0.72 (((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z))))) <=> ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1058,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1057])).
% 0.51/0.72 tff(1059,plain,
% 0.51/0.72 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z)))))),
% 0.51/0.72 inference(transitivity,[status(thm)],[1058, 1056])).
% 0.51/0.72 tff(1060,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(z)))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1061,plain,
% 0.51/0.72 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1060, 1059])).
% 0.51/0.72 tff(1062,plain,
% 0.51/0.72 ($false),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1061, 371, 443, 434, 1055])).
% 0.51/0.72 tff(1063,plain,((~r(z, elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.72 tff(1064,plain,
% 0.51/0.72 (~r(z, s(s(z)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1063, 971, 443])).
% 0.51/0.72 tff(1065,plain,
% 0.51/0.72 ((z = s(s(z))) <=> (s(s(z)) = z)),
% 0.51/0.72 inference(commutativity,[status(thm)],[])).
% 0.51/0.72 tff(1066,plain,
% 0.51/0.72 ((s(s(z)) = z) <=> (z = s(s(z)))),
% 0.51/0.72 inference(symmetry,[status(thm)],[1065])).
% 0.51/0.72 tff(1067,plain,
% 0.51/0.72 ((~(s(s(z)) = z)) <=> (~(z = s(s(z))))),
% 0.51/0.72 inference(monotonicity,[status(thm)],[1066])).
% 0.51/0.72 tff(1068,plain,
% 0.51/0.72 (~(z = s(s(z)))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[194, 1067])).
% 0.51/0.72 tff(1069,plain,
% 0.51/0.72 (((~![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))))),
% 0.51/0.72 inference(rewrite,[status(thm)],[])).
% 0.51/0.72 tff(1070,plain,
% 0.51/0.72 ((~![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))))),
% 0.51/0.72 inference(quant_inst,[status(thm)],[])).
% 0.51/0.72 tff(1071,plain,
% 0.51/0.72 ((~![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)))),
% 0.51/0.72 inference(modus_ponens,[status(thm)],[1070, 1069])).
% 0.51/0.72 tff(1072,plain,
% 0.51/0.72 ((z = s(s(z))) | b(z, s(s(z))) | r(z, s(s(z)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1071, 139])).
% 0.51/0.72 tff(1073,plain,
% 0.51/0.72 (b(z, s(s(z))) | r(z, s(s(z)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1072, 1068])).
% 0.51/0.72 tff(1074,plain,
% 0.51/0.72 (b(z, s(s(z)))),
% 0.51/0.72 inference(unit_resolution,[status(thm)],[1073, 1064])).
% 0.51/0.72 tff(1075,plain,
% 0.51/0.72 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1076,plain,
% 0.51/0.73 (((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1077,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))))),
% 0.51/0.73 inference(monotonicity,[status(thm)],[1076])).
% 0.51/0.73 tff(1078,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.73 inference(transitivity,[status(thm)],[1077, 1075])).
% 0.51/0.73 tff(1079,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(z)))) | (~b(s(elem!1), z)))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1080,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1079, 1078])).
% 0.51/0.73 tff(1081,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1080, 272, 1074, 925, 1054, 1018])).
% 0.51/0.73 tff(1082,plain,((~r(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(z), elem!1)) | (elem!1 = z) | (s(elem!1) = s(s(z))) | b(s(s(z)), elem!1) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1083,plain,
% 0.51/0.73 (~r(z, elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1082, 923, 253, 260, 248, 897, 221, 844])).
% 0.51/0.73 tff(1084,plain,
% 0.51/0.73 (b(z, elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[432, 1083, 261])).
% 0.51/0.73 tff(1085,plain,
% 0.51/0.73 (~b(s(z), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[279, 1084, 253])).
% 0.51/0.73 tff(1086,plain,
% 0.51/0.73 (r(s(z), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[289, 1085])).
% 0.51/0.73 tff(1087,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1088,plain,
% 0.51/0.73 (((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1089,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))))),
% 0.51/0.73 inference(monotonicity,[status(thm)],[1088])).
% 0.51/0.73 tff(1090,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.51/0.73 inference(transitivity,[status(thm)],[1089, 1087])).
% 0.51/0.73 tff(1091,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z)))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1092,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), z))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1091, 1090])).
% 0.51/0.73 tff(1093,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1092, 272, 262, 864, 1030])).
% 0.51/0.73 tff(1094,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1095,plain,
% 0.51/0.73 (~b(s(s(elem!1)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1094, 1084, 844])).
% 0.51/0.73 tff(1096,plain,
% 0.51/0.73 (r(s(s(elem!1)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[453, 1095])).
% 0.51/0.73 tff(1097,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1027, 1096, 1086, 863])).
% 0.51/0.73 tff(1098,plain,((~b(s(z), elem!1)) | (s(elem!1) = s(s(z))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1099,plain,
% 0.51/0.73 (~b(s(z), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1098, 203, 221, 248])).
% 0.51/0.73 tff(1100,plain,
% 0.51/0.73 (r(s(z), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[143, 1099, 252])).
% 0.51/0.73 tff(1101,assumption,(r(s(z), elem!1)), introduced(assumption)).
% 0.51/0.73 tff(1102,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1103,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1104,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1103, 1102])).
% 0.51/0.73 tff(1105,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1104, 371, 1101, 637, 361])).
% 0.51/0.73 tff(1106,plain,((~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1107,plain,
% 0.51/0.73 (~r(s(elem!1), s(z))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1106, 637, 1100])).
% 0.51/0.73 tff(1108,plain,
% 0.51/0.73 (b(s(elem!1), s(z))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[324, 1107, 259])).
% 0.51/0.73 tff(1109,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1110,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1111,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1110, 1109])).
% 0.51/0.73 tff(1112,plain,
% 0.51/0.73 (~r(s(s(z)), s(z))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1111, 371, 434, 1101])).
% 0.51/0.73 tff(1113,plain,
% 0.51/0.73 (b(s(s(z)), s(z))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[359, 1112])).
% 0.51/0.73 tff(1114,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1115,plain,
% 0.51/0.73 (((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1116,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))))),
% 0.51/0.73 inference(monotonicity,[status(thm)],[1115])).
% 0.51/0.73 tff(1117,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.51/0.73 inference(transitivity,[status(thm)],[1116, 1114])).
% 0.51/0.73 tff(1118,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1119,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(z)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1118, 1117])).
% 0.51/0.73 tff(1120,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1119, 272, 308, 1113, 642])).
% 0.51/0.73 tff(1121,plain,((~r(s(s(z)), elem!1)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1122,plain,
% 0.51/0.73 (~r(s(s(z)), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1121, 1108, 248, 637, 1100])).
% 0.51/0.73 tff(1123,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1124,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1125,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(elem!1)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1124, 1123])).
% 0.51/0.73 tff(1126,plain,
% 0.51/0.73 (~r(s(z), s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1125, 371, 1101, 637])).
% 0.51/0.73 tff(1127,plain,
% 0.51/0.73 ((s(z) = s(elem!1)) | b(s(z), s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[305, 139, 1126])).
% 0.51/0.73 tff(1128,plain,
% 0.51/0.73 (b(s(z), s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1127, 295])).
% 0.51/0.73 tff(1129,assumption,(~r(s(s(z)), elem!1)), introduced(assumption)).
% 0.51/0.73 tff(1130,plain,
% 0.51/0.73 (~b(s(s(elem!1)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1094, 864, 262])).
% 0.51/0.73 tff(1131,plain,
% 0.51/0.73 (r(s(s(elem!1)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[453, 1130])).
% 0.51/0.73 tff(1132,plain,
% 0.51/0.73 (~b(s(s(z)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[787, 326, 262])).
% 0.51/0.73 tff(1133,plain,
% 0.51/0.73 (r(s(s(z)), z)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[462, 1132])).
% 0.51/0.73 tff(1134,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1135,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1)))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1136,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(elem!1))))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1135, 1134])).
% 0.51/0.73 tff(1137,plain,
% 0.51/0.73 (~r(s(s(z)), s(s(elem!1)))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1136, 371, 1133, 1131])).
% 0.51/0.73 tff(1138,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[441, 139, 203, 871, 1137])).
% 0.51/0.73 tff(1139,plain,((~b(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1140,plain,
% 0.51/0.73 (~b(s(s(z)), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1139, 864, 203, 262])).
% 0.51/0.73 tff(1141,plain,
% 0.51/0.73 (s(s(z)) = elem!1),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[476, 1140, 1129])).
% 0.51/0.73 tff(1142,plain,
% 0.51/0.73 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[495, 1141])).
% 0.51/0.73 tff(1143,plain,
% 0.51/0.73 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[502, 1142])).
% 0.51/0.73 tff(1144,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1145,plain,
% 0.51/0.73 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1146,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.73 inference(monotonicity,[status(thm)],[1145])).
% 0.51/0.73 tff(1147,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.73 inference(transitivity,[status(thm)],[1146, 1144])).
% 0.51/0.73 tff(1148,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1149,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(z), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1148, 1147])).
% 0.51/0.73 tff(1150,plain,
% 0.51/0.73 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1149, 371, 1101, 552])).
% 0.51/0.73 tff(1151,plain,
% 0.51/0.73 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[538, 139, 155, 1150])).
% 0.51/0.73 tff(1152,assumption,(b(s(z), s(elem!1))), introduced(assumption)).
% 0.51/0.73 tff(1153,plain,
% 0.51/0.73 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1154,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1155,plain,
% 0.51/0.73 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1154, 1153])).
% 0.51/0.73 tff(1156,plain,
% 0.51/0.73 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1155, 371, 637, 552])).
% 0.51/0.73 tff(1157,plain,
% 0.51/0.73 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[527, 1156, 513])).
% 0.51/0.73 tff(1158,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1159,plain,
% 0.51/0.73 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1))))),
% 0.51/0.73 inference(rewrite,[status(thm)],[])).
% 0.51/0.73 tff(1160,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1)))))),
% 0.51/0.73 inference(monotonicity,[status(thm)],[1159])).
% 0.51/0.73 tff(1161,plain,
% 0.51/0.73 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1))))),
% 0.51/0.73 inference(transitivity,[status(thm)],[1160, 1158])).
% 0.51/0.73 tff(1162,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.73 inference(quant_inst,[status(thm)],[])).
% 0.51/0.73 tff(1163,plain,
% 0.51/0.73 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(elem!1)))),
% 0.51/0.73 inference(modus_ponens,[status(thm)],[1162, 1161])).
% 0.51/0.73 tff(1164,plain,
% 0.51/0.73 ($false),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1163, 272, 1157, 1152, 1151])).
% 0.51/0.73 tff(1165,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(z), s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.73 tff(1166,plain,
% 0.51/0.73 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[1165, 1143, 1128, 1101, 637])).
% 0.51/0.73 tff(1167,plain,
% 0.51/0.73 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.73 inference(unit_resolution,[status(thm)],[545, 1166, 221])).
% 0.51/0.74 tff(1168,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1169,plain,
% 0.51/0.74 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1170,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1169])).
% 0.51/0.74 tff(1171,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.74 inference(transitivity,[status(thm)],[1170, 1168])).
% 0.51/0.74 tff(1172,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1173,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1172, 1171])).
% 0.51/0.74 tff(1174,plain,
% 0.51/0.74 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1173, 272, 864, 1167])).
% 0.51/0.74 tff(1175,plain,
% 0.51/0.74 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[607, 1141])).
% 0.51/0.74 tff(1176,plain,
% 0.51/0.74 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[611, 139, 1175, 1174])).
% 0.51/0.74 tff(1177,plain,
% 0.51/0.74 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[669, 272, 262, 1167])).
% 0.51/0.74 tff(1178,plain,
% 0.51/0.74 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[562, 1177])).
% 0.51/0.74 tff(1179,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1180,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1181,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1180, 1179])).
% 0.51/0.74 tff(1182,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1181, 371, 1131, 1178, 1176])).
% 0.51/0.74 tff(1183,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(z), elem!1)) | (~r(s(elem!1), elem!1)) | r(s(s(z)), elem!1) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1184,plain,
% 0.51/0.74 (~b(s(s(elem!1)), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1183, 637, 221, 1100, 262, 1122, 203])).
% 0.51/0.74 tff(1185,plain,
% 0.51/0.74 (r(s(s(elem!1)), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[843, 1184, 231])).
% 0.51/0.74 tff(1186,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1187,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1188,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(z)))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1187, 1186])).
% 0.51/0.74 tff(1189,plain,
% 0.51/0.74 (~r(s(s(elem!1)), s(z))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1188, 371, 1100, 1185])).
% 0.51/0.74 tff(1190,plain,
% 0.51/0.74 (b(s(s(elem!1)), s(z))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[890, 1189])).
% 0.51/0.74 tff(1191,plain,
% 0.51/0.74 (~r(s(s(elem!1)), s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[655, 371, 1185, 637])).
% 0.51/0.74 tff(1192,plain,
% 0.51/0.74 (b(s(s(elem!1)), s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[660, 1191, 237])).
% 0.51/0.74 tff(1193,assumption,(b(s(s(elem!1)), s(z))), introduced(assumption)).
% 0.51/0.74 tff(1194,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1195,plain,
% 0.51/0.74 (((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1196,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z)))))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1195])).
% 0.51/0.74 tff(1197,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))))),
% 0.51/0.74 inference(transitivity,[status(thm)],[1196, 1194])).
% 0.51/0.74 tff(1198,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1199,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z))) | (~b(s(elem!1), s(z)))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1198, 1197])).
% 0.51/0.74 tff(1200,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1199, 272, 717, 308, 1193])).
% 0.51/0.74 tff(1201,plain,((~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1202,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1201, 1192, 1190, 1108])).
% 0.51/0.74 tff(1203,plain,((~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(z, elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1204,plain,
% 0.51/0.74 (~r(s(elem!1), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1203, 262, 221, 203, 248])).
% 0.51/0.74 tff(1205,plain,
% 0.51/0.74 (b(s(elem!1), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[618, 1204, 247])).
% 0.51/0.74 tff(1206,plain,
% 0.51/0.74 (~b(s(elem!1), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[407, 291, 262])).
% 0.51/0.74 tff(1207,plain,
% 0.51/0.74 (r(s(elem!1), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[414, 1206])).
% 0.51/0.74 tff(1208,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1209,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z)))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1210,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(z))))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1209, 1208])).
% 0.51/0.74 tff(1211,plain,
% 0.51/0.74 (~r(s(elem!1), s(s(z)))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1210, 371, 1133, 1207])).
% 0.51/0.74 tff(1212,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[336, 139, 248, 333, 1211])).
% 0.51/0.74 tff(1213,plain,((~b(s(s(z)), elem!1)) | (s(elem!1) = s(s(z))) | (~b(s(elem!1), elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1214,plain,
% 0.51/0.74 (~b(s(s(z)), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1213, 1205, 248, 262])).
% 0.51/0.74 tff(1215,assumption,(r(s(s(elem!1)), s(elem!1))), introduced(assumption)).
% 0.51/0.74 tff(1216,plain,
% 0.51/0.74 (~b(s(s(elem!1)), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1094, 262, 864])).
% 0.51/0.74 tff(1217,plain,
% 0.51/0.74 (r(s(s(elem!1)), z)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[453, 1216])).
% 0.51/0.74 tff(1218,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1219,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1220,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1)))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1219, 1218])).
% 0.51/0.74 tff(1221,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1220, 371, 1215, 416, 1019])).
% 0.51/0.74 tff(1222,plain,((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1223,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1222, 415, 1217, 1215])).
% 0.51/0.74 tff(1224,plain,((~b(z, elem!1)) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1225,plain,
% 0.51/0.74 (~r(s(s(elem!1)), s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1224, 864, 262, 291])).
% 0.51/0.74 tff(1226,plain,
% 0.51/0.74 (b(s(s(elem!1)), s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[660, 1225, 244])).
% 0.51/0.74 tff(1227,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1228,plain,
% 0.51/0.74 (((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1229,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1228])).
% 0.51/0.74 tff(1230,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(transitivity,[status(thm)],[1229, 1227])).
% 0.51/0.74 tff(1231,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1232,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), elem!1))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1231, 1230])).
% 0.51/0.74 tff(1233,plain,
% 0.51/0.74 ($false),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1232, 272, 1226, 864, 291])).
% 0.51/0.74 tff(1234,plain,((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.74 tff(1235,plain,
% 0.51/0.74 (~b(s(s(elem!1)), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1234, 1205, 237, 262])).
% 0.51/0.74 tff(1236,plain,
% 0.51/0.74 (r(s(s(elem!1)), elem!1)),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[843, 1235, 231])).
% 0.51/0.74 tff(1237,plain,
% 0.51/0.74 ((z = s(elem!1)) <=> (s(elem!1) = z)),
% 0.51/0.74 inference(commutativity,[status(thm)],[])).
% 0.51/0.74 tff(1238,plain,
% 0.51/0.74 ((s(elem!1) = z) <=> (z = s(elem!1))),
% 0.51/0.74 inference(symmetry,[status(thm)],[1237])).
% 0.51/0.74 tff(1239,plain,
% 0.51/0.74 ((~(s(elem!1) = z)) <=> (~(z = s(elem!1)))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1238])).
% 0.51/0.74 tff(1240,plain,
% 0.51/0.74 (~(z = s(elem!1))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[410, 1239])).
% 0.51/0.74 tff(1241,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1242,plain,
% 0.51/0.74 (((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1)))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1243,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1242])).
% 0.51/0.74 tff(1244,plain,
% 0.51/0.74 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1)))),
% 0.51/0.74 inference(transitivity,[status(thm)],[1243, 1241])).
% 0.51/0.74 tff(1245,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (~b(z, s(elem!1))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1246,plain,
% 0.51/0.74 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(elem!1), elem!1))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1245, 1244])).
% 0.51/0.74 tff(1247,plain,
% 0.51/0.74 (~b(z, s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1246, 272, 262, 291])).
% 0.51/0.74 tff(1248,plain,
% 0.51/0.74 (((~![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)))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1249,plain,
% 0.51/0.74 ((~![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)))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1250,plain,
% 0.51/0.74 ((~![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))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1249, 1248])).
% 0.51/0.74 tff(1251,plain,
% 0.51/0.74 ((z = s(elem!1)) | r(z, s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1250, 139, 1247])).
% 0.51/0.74 tff(1252,plain,
% 0.51/0.74 (r(z, s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[1251, 1240])).
% 0.51/0.74 tff(1253,plain,
% 0.51/0.74 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.51/0.74 inference(unit_resolution,[status(thm)],[502, 927])).
% 0.51/0.74 tff(1254,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1255,plain,
% 0.51/0.74 (((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1))))) <=> ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.74 inference(rewrite,[status(thm)],[])).
% 0.51/0.74 tff(1256,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))))),
% 0.51/0.74 inference(monotonicity,[status(thm)],[1255])).
% 0.51/0.74 tff(1257,plain,
% 0.51/0.74 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.74 inference(transitivity,[status(thm)],[1256, 1254])).
% 0.51/0.74 tff(1258,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(elem!1)))))),
% 0.51/0.74 inference(quant_inst,[status(thm)],[])).
% 0.51/0.74 tff(1259,plain,
% 0.51/0.74 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), s(s(elem!1))))),
% 0.51/0.74 inference(modus_ponens,[status(thm)],[1258, 1257])).
% 0.51/0.75 tff(1260,plain,
% 0.51/0.75 (~r(s(z), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1259, 371, 1101, 254])).
% 0.51/0.75 tff(1261,plain,
% 0.51/0.75 (b(s(z), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[862, 1260])).
% 0.51/0.75 tff(1262,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1263,plain,
% 0.51/0.75 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1264,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 0.51/0.75 inference(monotonicity,[status(thm)],[1263])).
% 0.51/0.75 tff(1265,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.75 inference(transitivity,[status(thm)],[1264, 1262])).
% 0.51/0.75 tff(1266,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1267,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1266, 1265])).
% 0.51/0.75 tff(1268,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1267, 272, 1261, 684, 1151])).
% 0.51/0.75 tff(1269,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1270,plain,
% 0.51/0.75 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1269, 967, 1101, 254])).
% 0.51/0.75 tff(1271,plain,
% 0.51/0.75 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[545, 1270, 221])).
% 0.51/0.75 tff(1272,plain,
% 0.51/0.75 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[522, 1271, 291])).
% 0.51/0.75 tff(1273,plain,
% 0.51/0.75 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[527, 1272, 1253])).
% 0.51/0.75 tff(1274,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1275,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1276,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1275, 1274])).
% 0.51/0.75 tff(1277,plain,
% 0.51/0.75 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1276, 371, 1273, 1252])).
% 0.51/0.75 tff(1278,plain,
% 0.51/0.75 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[669, 272, 262, 1271])).
% 0.51/0.75 tff(1279,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[562, 1278, 1277])).
% 0.51/0.75 tff(1280,plain,((~(s(s(z)) = elem!1)) | (~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~r(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1281,plain,
% 0.51/0.75 (~(s(s(z)) = elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1280, 1236, 1205, 221, 1100, 262])).
% 0.51/0.75 tff(1282,plain,
% 0.51/0.75 (r(s(s(z)), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[476, 1281, 1214])).
% 0.51/0.75 tff(1283,plain,
% 0.51/0.75 (~r(s(s(z)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1111, 371, 1282, 1100])).
% 0.51/0.75 tff(1284,plain,
% 0.51/0.75 (b(s(s(z)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[359, 1283])).
% 0.51/0.75 tff(1285,plain,
% 0.51/0.75 (~r(s(s(elem!1)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1188, 371, 1100, 1236])).
% 0.51/0.75 tff(1286,plain,
% 0.51/0.75 (b(s(s(elem!1)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[890, 1285])).
% 0.51/0.75 tff(1287,plain,
% 0.51/0.75 (~r(s(s(z)), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[437, 371, 1282, 1236])).
% 0.51/0.75 tff(1288,plain,
% 0.51/0.75 (b(s(s(z)), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[441, 139, 203, 1287])).
% 0.51/0.75 tff(1289,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1290,plain,
% 0.51/0.75 (((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1))))) <=> ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1291,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))))),
% 0.51/0.75 inference(monotonicity,[status(thm)],[1290])).
% 0.51/0.75 tff(1292,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(transitivity,[status(thm)],[1291, 1289])).
% 0.51/0.75 tff(1293,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(s(s(z)), s(s(elem!1)))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1294,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(s(elem!1)), s(z)))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1293, 1292])).
% 0.51/0.75 tff(1295,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1294, 272, 1288, 1286, 1284])).
% 0.51/0.75 tff(1296,plain,((~b(z, elem!1)) | (s(s(z)) = s(s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1297,plain,
% 0.51/0.75 (~b(z, elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1296, 203, 221, 248])).
% 0.51/0.75 tff(1298,plain,
% 0.51/0.75 (r(z, elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[432, 1297, 261])).
% 0.51/0.75 tff(1299,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1300,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1301,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1300, 1299])).
% 0.51/0.75 tff(1302,plain,
% 0.51/0.75 (~r(s(z), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1301, 371, 443, 1101])).
% 0.51/0.75 tff(1303,plain,
% 0.51/0.75 (b(s(z), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[289, 1302])).
% 0.51/0.75 tff(1304,plain,
% 0.51/0.75 (~r(s(elem!1), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1106, 637, 1101])).
% 0.51/0.75 tff(1305,plain,
% 0.51/0.75 (b(s(elem!1), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[324, 1304, 11])).
% 0.51/0.75 tff(1306,plain,
% 0.51/0.75 (~r(s(elem!1), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[828, 637, 443])).
% 0.51/0.75 tff(1307,plain,
% 0.51/0.75 (b(s(elem!1), z)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[414, 1306])).
% 0.51/0.75 tff(1308,assumption,(b(s(z), z)), introduced(assumption)).
% 0.51/0.75 tff(1309,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1310,plain,
% 0.51/0.75 (((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1311,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))))),
% 0.51/0.75 inference(monotonicity,[status(thm)],[1310])).
% 0.51/0.75 tff(1312,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z))))),
% 0.51/0.75 inference(transitivity,[status(thm)],[1311, 1309])).
% 0.51/0.75 tff(1313,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), s(z))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1314,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1313, 1312])).
% 0.51/0.75 tff(1315,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1314, 272, 1308, 399, 308])).
% 0.51/0.75 tff(1316,plain,((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1317,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1316, 1307, 1305, 1303])).
% 0.51/0.75 tff(1318,plain,((~r(s(elem!1), elem!1)) | (s(elem!1) = s(z)) | (~r(z, elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1319,plain,
% 0.51/0.75 (~r(s(elem!1), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1318, 259, 1298, 1100])).
% 0.51/0.75 tff(1320,plain,
% 0.51/0.75 (b(s(elem!1), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[618, 1319, 247])).
% 0.51/0.75 tff(1321,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1322,plain,
% 0.51/0.75 (((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z)))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1323,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))))),
% 0.51/0.75 inference(monotonicity,[status(thm)],[1322])).
% 0.51/0.75 tff(1324,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1)))),
% 0.51/0.75 inference(transitivity,[status(thm)],[1323, 1321])).
% 0.51/0.75 tff(1325,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(z, elem!1)) | (~r(z, s(z))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1326,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(s(z), elem!1))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1325, 1324])).
% 0.51/0.75 tff(1327,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1326, 371, 443, 1101, 417])).
% 0.51/0.75 tff(1328,plain,((~r(z, elem!1)) | (~r(s(z), elem!1)) | (~r(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1329,plain,
% 0.51/0.75 (~r(z, s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1328, 443, 1101])).
% 0.51/0.75 tff(1330,plain,
% 0.51/0.75 (b(z, s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[397, 1329])).
% 0.51/0.75 tff(1331,plain,
% 0.51/0.75 (~r(s(s(elem!1)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1188, 371, 1101, 254])).
% 0.51/0.75 tff(1332,plain,
% 0.51/0.75 (b(s(s(elem!1)), s(z))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[890, 1331])).
% 0.51/0.75 tff(1333,assumption,(b(z, s(z))), introduced(assumption)).
% 0.51/0.75 tff(1334,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1335,plain,
% 0.51/0.75 (((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z))) <=> ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1336,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))))),
% 0.51/0.75 inference(monotonicity,[status(thm)],[1335])).
% 0.51/0.75 tff(1337,plain,
% 0.51/0.75 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z))))),
% 0.51/0.75 inference(transitivity,[status(thm)],[1336, 1334])).
% 0.51/0.75 tff(1338,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(elem!1)), s(z))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1339,plain,
% 0.51/0.75 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1338, 1337])).
% 0.51/0.75 tff(1340,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1339, 272, 1333, 1030, 1193])).
% 0.51/0.75 tff(1341,plain,((~b(z, s(z))) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1342,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1341, 1332, 454, 1330])).
% 0.51/0.75 tff(1343,plain,((~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1344,plain,
% 0.51/0.75 (~r(s(s(elem!1)), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1343, 1100, 1298])).
% 0.51/0.75 tff(1345,plain,
% 0.51/0.75 (b(s(s(elem!1)), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[843, 1344, 231])).
% 0.51/0.75 tff(1346,assumption,(~(s(s(z)) = elem!1)), introduced(assumption)).
% 0.51/0.75 tff(1347,plain,
% 0.51/0.75 (~(s(elem!1) = s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[623, 244])).
% 0.51/0.75 tff(1348,plain,
% 0.51/0.75 (~b(s(elem!1), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[919, 272, 864, 291])).
% 0.51/0.75 tff(1349,plain,
% 0.51/0.75 (r(s(elem!1), s(s(elem!1)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[635, 1348, 1347])).
% 0.51/0.75 tff(1350,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1351,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z)))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1352,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), s(s(z))))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1351, 1350])).
% 0.51/0.75 tff(1353,plain,
% 0.51/0.75 ($false),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1352, 371, 902, 872, 337])).
% 0.51/0.75 tff(1354,plain,((~b(s(s(z)), elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(elem!1) = s(s(z))) | (s(s(z)) = s(s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.75 tff(1355,plain,
% 0.51/0.75 (~b(s(s(z)), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1354, 1349, 248, 203, 864, 291])).
% 0.51/0.75 tff(1356,plain,
% 0.51/0.75 (r(s(s(z)), elem!1)),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[476, 1355, 1346])).
% 0.51/0.75 tff(1357,plain,
% 0.51/0.75 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 0.51/0.75 inference(rewrite,[status(thm)],[])).
% 0.51/0.75 tff(1358,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z)))))),
% 0.51/0.75 inference(quant_inst,[status(thm)],[])).
% 0.51/0.75 tff(1359,plain,
% 0.51/0.75 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(z))))),
% 0.51/0.75 inference(modus_ponens,[status(thm)],[1358, 1357])).
% 0.51/0.75 tff(1360,plain,
% 0.51/0.75 (~r(s(z), s(s(z)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[1359, 371, 1356, 1101])).
% 0.51/0.75 tff(1361,plain,
% 0.51/0.75 (b(s(z), s(s(z)))),
% 0.51/0.75 inference(unit_resolution,[status(thm)],[804, 1360])).
% 0.51/0.76 tff(1362,assumption,(~(z = elem!1)), introduced(assumption)).
% 0.51/0.76 tff(1363,plain,
% 0.51/0.76 (~b(s(s(elem!1)), s(elem!1))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1232, 272, 864, 291])).
% 0.51/0.76 tff(1364,plain,
% 0.51/0.76 (r(s(s(elem!1)), s(elem!1))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[660, 1363, 244])).
% 0.51/0.76 tff(1365,plain,
% 0.51/0.76 (~b(z, elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1224, 1364, 291, 864])).
% 0.51/0.76 tff(1366,plain,
% 0.51/0.76 (r(z, elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[432, 1365, 1362])).
% 0.51/0.76 tff(1367,plain,
% 0.51/0.76 (~r(z, s(s(z)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1063, 1366, 1356])).
% 0.51/0.76 tff(1368,plain,
% 0.51/0.76 (b(z, s(s(z)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1073, 1367])).
% 0.51/0.76 tff(1369,plain,
% 0.51/0.76 (~r(z, s(z))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1328, 1366, 1101])).
% 0.51/0.76 tff(1370,plain,
% 0.51/0.76 (b(z, s(z))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[397, 1369])).
% 0.51/0.76 tff(1371,assumption,(b(z, s(s(z)))), introduced(assumption)).
% 0.51/0.76 tff(1372,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1373,plain,
% 0.51/0.76 (((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z)))) <=> ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1374,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1373])).
% 0.51/0.76 tff(1375,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z)))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[1374, 1372])).
% 0.51/0.76 tff(1376,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(z), s(s(z)))) | (~b(z, s(z))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1377,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(z))) | (~b(s(z), s(s(z)))) | (~b(z, s(s(z))))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1376, 1375])).
% 0.51/0.76 tff(1378,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1377, 272, 790, 1371, 1333])).
% 0.51/0.76 tff(1379,plain,((~b(s(z), s(s(z)))) | (~b(z, s(s(z)))) | (~b(z, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1380,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1379, 1370, 1368, 1361])).
% 0.51/0.76 tff(1381,plain,((~b(s(elem!1), elem!1)) | (~r(s(z), elem!1)) | (z = elem!1) | (~b(s(s(elem!1)), elem!1)) | (s(s(z)) = elem!1) | (s(elem!1) = s(s(z))) | (s(s(z)) = s(s(elem!1))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1382,plain,
% 0.51/0.76 (s(s(z)) = elem!1),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1381, 1345, 261, 1100, 1320, 248, 203, 237])).
% 0.51/0.76 tff(1383,plain,
% 0.51/0.76 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[495, 1382])).
% 0.51/0.76 tff(1384,plain,
% 0.51/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[502, 1383])).
% 0.51/0.76 tff(1385,plain,
% 0.51/0.76 (~b(s(s(elem!1)), s(elem!1))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1232, 272, 1345, 1320])).
% 0.51/0.76 tff(1386,plain,
% 0.51/0.76 (r(s(s(elem!1)), s(elem!1))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[660, 1385, 237])).
% 0.51/0.76 tff(1387,plain,
% 0.51/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[607, 1382])).
% 0.51/0.76 tff(1388,plain,
% 0.51/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1389,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1390,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1389, 1388])).
% 0.51/0.76 tff(1391,plain,
% 0.51/0.76 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1390, 371, 1215, 528])).
% 0.51/0.76 tff(1392,plain,
% 0.51/0.76 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1173, 272, 864, 504])).
% 0.51/0.76 tff(1393,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[611, 139, 662, 1392, 1391])).
% 0.51/0.76 tff(1394,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1395,plain,
% 0.51/0.76 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1394, 1387, 1386, 1345, 1384, 1320])).
% 0.51/0.76 tff(1396,plain,
% 0.51/0.76 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[545, 1395, 221])).
% 0.51/0.76 tff(1397,plain,
% 0.51/0.76 (~r(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1149, 371, 1100, 1396])).
% 0.51/0.76 tff(1398,plain,
% 0.51/0.76 (b(s(z), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[538, 139, 155, 1397])).
% 0.51/0.76 tff(1399,plain,
% 0.51/0.76 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[555, 371, 1298, 1396])).
% 0.51/0.76 tff(1400,plain,
% 0.51/0.76 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[562, 1399])).
% 0.51/0.76 tff(1401,plain,
% 0.51/0.76 (~r(s(z), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1301, 371, 1298, 1100])).
% 0.51/0.76 tff(1402,plain,
% 0.51/0.76 (b(s(z), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[289, 1401])).
% 0.51/0.76 tff(1403,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1404,plain,
% 0.51/0.76 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1405,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1404])).
% 0.51/0.76 tff(1406,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.76 inference(transitivity,[status(thm)],[1405, 1403])).
% 0.51/0.76 tff(1407,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1408,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(z), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1407, 1406])).
% 0.51/0.76 tff(1409,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1408, 272, 1402, 1400, 1398])).
% 0.51/0.76 tff(1410,plain,((s(s(z)) = s(s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1411,plain,
% 0.51/0.76 (s(elem!1) = s(s(z))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1410, 220, 203])).
% 0.51/0.76 tff(1412,assumption,(s(elem!1) = s(s(z))), introduced(assumption)).
% 0.51/0.76 tff(1413,plain,
% 0.51/0.76 (s(s(z)) = s(elem!1)),
% 0.51/0.76 inference(symmetry,[status(thm)],[1412])).
% 0.51/0.76 tff(1414,plain,
% 0.51/0.76 (inj_0(s(s(z))) = inj_0(s(elem!1))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1413])).
% 0.51/0.76 tff(1415,plain,
% 0.51/0.76 (s(z) = elem!1),
% 0.51/0.76 inference(transitivity,[status(thm)],[213, 1414, 88])).
% 0.51/0.76 tff(1416,assumption,(~(s(z) = elem!1)), introduced(assumption)).
% 0.51/0.76 tff(1417,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1416, 1415])).
% 0.51/0.76 tff(1418,plain,((~(s(elem!1) = s(s(z)))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1419,plain,
% 0.51/0.76 (s(z) = elem!1),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1418, 1411])).
% 0.51/0.76 tff(1420,plain,
% 0.51/0.76 (s(z) = s(s(z))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1419, 206])).
% 0.51/0.76 tff(1421,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[353, 1420])).
% 0.51/0.76 tff(1422,plain,((~(s(s(z)) = elem!1)) | (s(s(z)) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1423,plain,
% 0.51/0.76 (~(s(s(z)) = elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1422, 203])).
% 0.51/0.76 tff(1424,plain,
% 0.51/0.76 (r(s(s(z)), elem!1)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[476, 1423, 202])).
% 0.51/0.76 tff(1425,plain,
% 0.51/0.76 (r(s(elem!1), s(z))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1424, 201])).
% 0.51/0.76 tff(1426,plain,
% 0.51/0.76 (r(s(elem!1), elem!1)),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1424, 200])).
% 0.51/0.76 tff(1427,plain,
% 0.51/0.76 (elem!1 = s(z)),
% 0.51/0.76 inference(symmetry,[status(thm)],[53])).
% 0.51/0.76 tff(1428,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(elem!1))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[721])).
% 0.51/0.76 tff(1429,plain,
% 0.51/0.76 (s(s(s(s(s(elem!1))))) = s(z)),
% 0.51/0.76 inference(transitivity,[status(thm)],[33, 1428, 88, 1427])).
% 0.51/0.76 tff(1430,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(z))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1429])).
% 0.51/0.76 tff(1431,plain,
% 0.51/0.76 (s(s(s(s(elem!1)))) = z),
% 0.51/0.76 inference(transitivity,[status(thm)],[38, 1430, 24])).
% 0.51/0.76 tff(1432,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[48, 1431])).
% 0.51/0.76 tff(1433,plain,((~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1434,plain,
% 0.51/0.76 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1433, 53])).
% 0.51/0.76 tff(1435,plain,
% 0.51/0.76 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1436,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1435, 22])).
% 0.51/0.76 tff(1437,assumption,(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.51/0.76 tff(1438,plain,
% 0.51/0.76 (s(s(s(s(s(s(s(elem!1))))))) = s(s(elem!1))),
% 0.51/0.76 inference(symmetry,[status(thm)],[1437])).
% 0.51/0.76 tff(1439,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(elem!1)))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1438])).
% 0.51/0.76 tff(1440,plain,
% 0.51/0.76 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.76 inference(symmetry,[status(thm)],[1439])).
% 0.51/0.76 tff(1441,plain,
% 0.51/0.76 (s(elem!1) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[68, 1440, 1436])).
% 0.51/0.76 tff(1442,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[500, 1441])).
% 0.51/0.76 tff(1443,plain,((~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))) | (s(elem!1) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1444,plain,
% 0.51/0.76 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1443, 1434])).
% 0.51/0.76 tff(1445,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))), introduced(assumption)).
% 0.51/0.76 tff(1446,plain,
% 0.51/0.76 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(symmetry,[status(thm)],[1445])).
% 0.51/0.76 tff(1447,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1446])).
% 0.51/0.76 tff(1448,plain,
% 0.51/0.76 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[33, 1447, 1436])).
% 0.51/0.76 tff(1449,plain,
% 0.51/0.76 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1448])).
% 0.51/0.76 tff(1450,plain,
% 0.51/0.76 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[38, 1449, 1447, 1436])).
% 0.51/0.76 tff(1451,plain,
% 0.51/0.76 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1450])).
% 0.51/0.76 tff(1452,plain,
% 0.51/0.76 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[165, 1451, 1447, 1436])).
% 0.51/0.76 tff(1453,plain,
% 0.51/0.76 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1452])).
% 0.51/0.76 tff(1454,plain,
% 0.51/0.76 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.51/0.76 inference(transitivity,[status(thm)],[602, 1453, 1447, 1436])).
% 0.51/0.76 tff(1455,plain,
% 0.51/0.76 ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1445])).
% 0.51/0.76 tff(1456,plain,
% 0.51/0.76 ((~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1455])).
% 0.51/0.76 tff(1457,assumption,(~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 0.51/0.76 tff(1458,plain,
% 0.51/0.76 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1457, 1456])).
% 0.51/0.76 tff(1459,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1458, 1454])).
% 0.51/0.76 tff(1460,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1461,plain,
% 0.51/0.76 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1460, 1444])).
% 0.51/0.76 tff(1462,plain,
% 0.51/0.76 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[53])).
% 0.51/0.76 tff(1463,plain,
% 0.51/0.76 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.51/0.76 inference(transitivity,[status(thm)],[1462, 127])).
% 0.51/0.76 tff(1464,plain,
% 0.51/0.76 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1463])).
% 0.51/0.76 tff(1465,plain,
% 0.51/0.76 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[155, 1464])).
% 0.51/0.76 tff(1466,plain,
% 0.51/0.76 (~(s(elem!1) = s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[623, 99])).
% 0.51/0.76 tff(1467,plain,
% 0.51/0.76 (r(s(z), s(s(elem!1))) <=> r(elem!1, s(s(elem!1)))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[53])).
% 0.51/0.76 tff(1468,plain,
% 0.51/0.76 (r(elem!1, s(s(elem!1))) <=> r(s(z), s(s(elem!1)))),
% 0.51/0.76 inference(symmetry,[status(thm)],[1467])).
% 0.51/0.76 tff(1469,plain,
% 0.51/0.76 (s(s(s(z))) = s(s(elem!1))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[54])).
% 0.51/0.76 tff(1470,plain,
% 0.51/0.76 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(elem!1)))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1469])).
% 0.51/0.76 tff(1471,plain,
% 0.51/0.76 (r(elem!1, s(s(s(z)))) <=> r(s(z), s(s(elem!1)))),
% 0.51/0.76 inference(transitivity,[status(thm)],[1470, 1468])).
% 0.51/0.76 tff(1472,assumption,(r(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.51/0.76 tff(1473,plain,
% 0.51/0.76 (r(s(z), s(s(elem!1)))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1472, 1471])).
% 0.51/0.76 tff(1474,plain,
% 0.51/0.76 (~r(s(elem!1), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[911, 1473, 361])).
% 0.51/0.76 tff(1475,plain,
% 0.51/0.76 (b(s(elem!1), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[635, 1474, 1466])).
% 0.51/0.76 tff(1476,plain,
% 0.51/0.76 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[172, 53])).
% 0.51/0.76 tff(1477,plain,
% 0.51/0.76 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[179, 1476])).
% 0.51/0.76 tff(1478,plain,
% 0.51/0.76 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[53])).
% 0.51/0.76 tff(1479,plain,
% 0.51/0.76 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.51/0.76 inference(transitivity,[status(thm)],[1478, 77])).
% 0.51/0.76 tff(1480,plain,
% 0.51/0.76 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1479])).
% 0.51/0.76 tff(1481,plain,
% 0.51/0.76 (~(s(s(elem!1)) = elem!1)),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[857, 1480])).
% 0.51/0.76 tff(1482,plain,
% 0.51/0.76 (r(elem!1, s(s(elem!1)))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1472, 1470])).
% 0.51/0.76 tff(1483,plain,
% 0.51/0.76 (r(s(z), z) <=> r(elem!1, z)),
% 0.51/0.76 inference(monotonicity,[status(thm)],[53])).
% 0.51/0.76 tff(1484,plain,
% 0.51/0.76 (r(elem!1, z) <=> r(s(z), z)),
% 0.51/0.76 inference(symmetry,[status(thm)],[1483])).
% 0.51/0.76 tff(1485,plain,
% 0.51/0.76 (r(s(z), z)),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[972, 1484])).
% 0.51/0.76 tff(1486,plain,
% 0.51/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1487,plain,
% 0.51/0.76 (((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1488,plain,
% 0.51/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1487])).
% 0.51/0.76 tff(1489,plain,
% 0.51/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z)))),
% 0.51/0.76 inference(transitivity,[status(thm)],[1488, 1486])).
% 0.51/0.76 tff(1490,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1491,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), z))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1490, 1489])).
% 0.51/0.76 tff(1492,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1491, 371, 972, 1047, 1019])).
% 0.51/0.76 tff(1493,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1494,plain,
% 0.51/0.76 (~r(s(s(elem!1)), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1493, 1047, 972])).
% 0.51/0.76 tff(1495,plain,
% 0.51/0.76 (b(s(s(elem!1)), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[453, 1494])).
% 0.51/0.76 tff(1496,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1497,plain,
% 0.51/0.76 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1498,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 0.51/0.76 inference(monotonicity,[status(thm)],[1497])).
% 0.51/0.76 tff(1499,plain,
% 0.51/0.76 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.51/0.76 inference(transitivity,[status(thm)],[1498, 1496])).
% 0.51/0.76 tff(1500,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1501,plain,
% 0.51/0.76 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1500, 1499])).
% 0.51/0.76 tff(1502,plain,
% 0.51/0.76 (~b(s(elem!1), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1501, 272, 399, 1495])).
% 0.51/0.76 tff(1503,plain,
% 0.51/0.76 (r(s(elem!1), s(s(elem!1)))),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[635, 1502, 898])).
% 0.51/0.76 tff(1504,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1050, 371, 1047, 637, 1503])).
% 0.51/0.76 tff(1505,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(elem!1) = s(s(elem!1))) | (~b(s(elem!1), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1506,plain,
% 0.51/0.76 (~b(s(elem!1), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1505, 972, 637, 1047, 1466])).
% 0.51/0.76 tff(1507,plain,
% 0.51/0.76 (r(s(elem!1), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[414, 1506])).
% 0.51/0.76 tff(1508,plain,
% 0.51/0.76 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.51/0.76 inference(rewrite,[status(thm)],[])).
% 0.51/0.76 tff(1509,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z))))),
% 0.51/0.76 inference(quant_inst,[status(thm)],[])).
% 0.51/0.76 tff(1510,plain,
% 0.51/0.76 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))),
% 0.51/0.76 inference(modus_ponens,[status(thm)],[1509, 1508])).
% 0.51/0.76 tff(1511,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1510, 371, 416, 361, 672])).
% 0.51/0.76 tff(1512,plain,((~r(s(z), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.76 tff(1513,plain,
% 0.51/0.76 (~r(s(z), z)),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1512, 1507, 361])).
% 0.51/0.76 tff(1514,plain,
% 0.51/0.76 ($false),
% 0.51/0.76 inference(unit_resolution,[status(thm)],[1513, 1485])).
% 0.51/0.76 tff(1515,plain,((~r(elem!1, z)) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(z))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1516,plain,
% 0.51/0.77 (~r(elem!1, z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1515, 1482, 361, 637, 53])).
% 0.51/0.77 tff(1517,plain,
% 0.51/0.77 (b(elem!1, z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[997, 1516, 5])).
% 0.51/0.77 tff(1518,plain,
% 0.51/0.77 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[502, 1434])).
% 0.51/0.77 tff(1519,plain,
% 0.51/0.77 (~(z = elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[7, 5])).
% 0.51/0.77 tff(1520,plain,
% 0.51/0.77 (b(z, s(s(s(z)))) <=> b(z, s(s(elem!1)))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1469])).
% 0.51/0.77 tff(1521,assumption,(r(z, s(s(s(z))))), introduced(assumption)).
% 0.51/0.77 tff(1522,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1523,plain,
% 0.51/0.77 (((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1524,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1523])).
% 0.51/0.77 tff(1525,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.51/0.77 inference(transitivity,[status(thm)],[1524, 1522])).
% 0.51/0.77 tff(1526,plain,
% 0.51/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))) | (~r(z, elem!1)))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1527,plain,
% 0.51/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1526, 1525])).
% 0.51/0.77 tff(1528,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1527, 371, 443, 1472, 1521])).
% 0.51/0.77 tff(1529,plain,((~r(z, s(s(s(z))))) | (~r(z, elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1530,plain,
% 0.51/0.77 (~r(z, s(s(s(z))))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1529, 443, 1472])).
% 0.51/0.77 tff(1531,plain,
% 0.51/0.77 ((z = s(s(s(z)))) <=> (s(s(s(z))) = z)),
% 0.51/0.77 inference(commutativity,[status(thm)],[])).
% 0.51/0.77 tff(1532,plain,
% 0.51/0.77 ((s(s(s(z))) = z) <=> (z = s(s(s(z))))),
% 0.51/0.77 inference(symmetry,[status(thm)],[1531])).
% 0.51/0.77 tff(1533,plain,
% 0.51/0.77 ((~(s(s(s(z))) = z)) <=> (~(z = s(s(s(z)))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1532])).
% 0.51/0.77 tff(1534,plain,
% 0.51/0.77 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(z))) = z))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1535,plain,
% 0.51/0.77 (~(s(s(s(z))) = z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1534, 46])).
% 0.51/0.77 tff(1536,plain,
% 0.51/0.77 (~(z = s(s(s(z))))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1535, 1533])).
% 0.51/0.77 tff(1537,plain,
% 0.51/0.77 (((~![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)))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1538,plain,
% 0.51/0.77 ((~![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)))))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1539,plain,
% 0.51/0.77 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1538, 1537])).
% 0.51/0.77 tff(1540,plain,
% 0.51/0.77 ((z = s(s(s(z)))) | b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1539, 139])).
% 0.51/0.77 tff(1541,plain,
% 0.51/0.77 (b(z, s(s(s(z)))) | r(z, s(s(s(z))))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1540, 1536])).
% 0.51/0.77 tff(1542,plain,
% 0.51/0.77 (b(z, s(s(s(z))))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1541, 1530])).
% 0.51/0.77 tff(1543,plain,
% 0.51/0.77 (b(z, s(s(elem!1)))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1542, 1520])).
% 0.51/0.77 tff(1544,assumption,(b(z, s(s(elem!1)))), introduced(assumption)).
% 0.51/0.77 tff(1545,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[836, 272, 399, 643, 1544])).
% 0.51/0.77 tff(1546,plain,((~b(z, s(s(elem!1)))) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1547,plain,
% 0.51/0.77 (~b(z, s(s(elem!1)))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1546, 925, 643])).
% 0.51/0.77 tff(1548,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1547, 1543])).
% 0.51/0.77 tff(1549,plain,((~r(z, elem!1)) | (~(s(z) = elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1550,plain,
% 0.51/0.77 (~r(z, elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1549, 1475, 53, 637, 1472])).
% 0.51/0.77 tff(1551,plain,
% 0.51/0.77 (b(z, elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[432, 1550, 1519])).
% 0.51/0.77 tff(1552,plain,
% 0.51/0.77 (~(s(elem!1) = elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[246, 244])).
% 0.51/0.77 tff(1553,plain,
% 0.51/0.77 ((elem!1 = s(elem!1)) <=> (s(elem!1) = elem!1)),
% 0.51/0.77 inference(symmetry,[status(thm)],[79])).
% 0.51/0.77 tff(1554,assumption,(elem!1 = s(elem!1)), introduced(assumption)).
% 0.51/0.77 tff(1555,plain,
% 0.51/0.77 (s(elem!1) = elem!1),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1554, 1553])).
% 0.51/0.77 tff(1556,assumption,(~(s(elem!1) = elem!1)), introduced(assumption)).
% 0.51/0.77 tff(1557,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1556, 1555])).
% 0.51/0.77 tff(1558,plain,((~(elem!1 = s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1559,plain,
% 0.51/0.77 (~(elem!1 = s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1558, 1552])).
% 0.51/0.77 tff(1560,plain,
% 0.51/0.77 (~r(s(elem!1), z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1222, 1019, 1215])).
% 0.51/0.77 tff(1561,plain,
% 0.51/0.77 (b(s(elem!1), z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[414, 1560])).
% 0.51/0.77 tff(1562,plain,
% 0.51/0.77 (~r(elem!1, z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1493, 1047, 1019])).
% 0.51/0.77 tff(1563,plain,
% 0.51/0.77 (b(elem!1, z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[997, 1562, 5])).
% 0.51/0.77 tff(1564,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1565,plain,
% 0.51/0.77 (((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1)))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1566,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1565])).
% 0.51/0.77 tff(1567,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z)))),
% 0.51/0.77 inference(transitivity,[status(thm)],[1566, 1564])).
% 0.51/0.77 tff(1568,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~b(elem!1, s(elem!1))))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1569,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(elem!1))) | (~b(s(elem!1), z))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1568, 1567])).
% 0.51/0.77 tff(1570,plain,
% 0.51/0.77 (~b(elem!1, s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1569, 272, 1563, 1561])).
% 0.51/0.77 tff(1571,plain,
% 0.51/0.77 (((~![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)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1572,plain,
% 0.51/0.77 ((~![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)))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1573,plain,
% 0.51/0.77 ((~![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))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1572, 1571])).
% 0.51/0.77 tff(1574,plain,
% 0.51/0.77 ((elem!1 = s(elem!1)) | b(elem!1, s(elem!1)) | r(elem!1, s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1573, 139])).
% 0.51/0.77 tff(1575,plain,
% 0.51/0.77 (r(elem!1, s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1574, 1570, 91])).
% 0.51/0.77 tff(1576,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1577,plain,
% 0.51/0.77 (((~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(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1578,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1577])).
% 0.51/0.77 tff(1579,plain,
% 0.51/0.77 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))))),
% 0.51/0.77 inference(transitivity,[status(thm)],[1578, 1576])).
% 0.51/0.77 tff(1580,plain,
% 0.51/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1))) | (~r(elem!1, s(s(elem!1)))))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1581,plain,
% 0.51/0.77 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(elem!1, s(elem!1)))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1580, 1579])).
% 0.51/0.77 tff(1582,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1581, 371, 1215, 1575, 1047])).
% 0.51/0.77 tff(1583,plain,((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (elem!1 = s(elem!1)) | (elem!1 = z) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1584,plain,
% 0.51/0.77 (~r(s(s(elem!1)), s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1583, 1019, 5, 1559, 1047])).
% 0.51/0.77 tff(1585,plain,
% 0.51/0.77 (b(s(s(elem!1)), s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[660, 1584, 244])).
% 0.51/0.77 tff(1586,assumption,(b(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.51/0.77 tff(1587,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1588,plain,
% 0.51/0.77 (((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1589,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1588])).
% 0.51/0.77 tff(1590,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(transitivity,[status(thm)],[1589, 1587])).
% 0.51/0.77 tff(1591,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1592,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1591, 1590])).
% 0.51/0.77 tff(1593,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1592, 272, 1032, 504, 1586])).
% 0.51/0.77 tff(1594,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1595,plain,
% 0.51/0.77 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1594, 504, 1032])).
% 0.51/0.77 tff(1596,plain,
% 0.51/0.77 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[562, 1595])).
% 0.51/0.77 tff(1597,plain,
% 0.51/0.77 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1181, 371, 1019, 1596])).
% 0.51/0.77 tff(1598,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1599,plain,
% 0.51/0.77 (((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1600,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1599])).
% 0.51/0.77 tff(1601,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.77 inference(transitivity,[status(thm)],[1600, 1598])).
% 0.51/0.77 tff(1602,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.77 inference(quant_inst,[status(thm)],[])).
% 0.51/0.77 tff(1603,plain,
% 0.51/0.77 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.51/0.77 inference(modus_ponens,[status(thm)],[1602, 1601])).
% 0.51/0.77 tff(1604,plain,
% 0.51/0.77 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1603, 272, 717, 864, 504])).
% 0.51/0.77 tff(1605,plain,
% 0.51/0.77 ($false),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[611, 139, 662, 1604, 1597])).
% 0.51/0.77 tff(1606,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.77 tff(1607,plain,
% 0.51/0.77 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1606, 1585, 1032, 662, 864, 1019])).
% 0.51/0.77 tff(1608,plain,
% 0.51/0.77 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[545, 1607, 221])).
% 0.51/0.77 tff(1609,plain,
% 0.51/0.77 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[1155, 371, 637, 1608])).
% 0.51/0.77 tff(1610,plain,
% 0.51/0.77 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.77 inference(unit_resolution,[status(thm)],[527, 1609, 513])).
% 0.51/0.77 tff(1611,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1612,plain,
% 0.51/0.77 (((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.77 inference(rewrite,[status(thm)],[])).
% 0.51/0.77 tff(1613,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 0.51/0.77 inference(monotonicity,[status(thm)],[1612])).
% 0.51/0.77 tff(1614,plain,
% 0.51/0.77 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.78 inference(transitivity,[status(thm)],[1613, 1611])).
% 0.51/0.78 tff(1615,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1616,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1615, 1614])).
% 0.51/0.78 tff(1617,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1616, 272, 717, 514, 551])).
% 0.51/0.78 tff(1618,plain,((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1619,plain,
% 0.51/0.78 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1618, 1610, 1585])).
% 0.51/0.78 tff(1620,plain,
% 0.51/0.78 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[611, 139, 662, 1619])).
% 0.51/0.78 tff(1621,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1622,plain,
% 0.51/0.78 (((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1623,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1622])).
% 0.51/0.78 tff(1624,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.51/0.78 inference(transitivity,[status(thm)],[1623, 1621])).
% 0.51/0.78 tff(1625,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1626,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 0.51/0.78 tff(1627,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1626, 371, 1047, 1608, 1620])).
% 0.51/0.78 tff(1628,plain,((~r(s(s(elem!1)), z)) | (~r(elem!1, s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(elem!1, z)) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1629,plain,
% 0.51/0.78 (~r(s(s(elem!1)), z)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1628, 864, 662, 513, 637, 221, 1032, 1047, 244, 5])).
% 0.51/0.78 tff(1630,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[453, 1130, 1629])).
% 0.51/0.78 tff(1631,plain,((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(elem!1, z)) | (~r(elem!1, s(s(elem!1)))) | (s(s(elem!1)) = s(elem!1)) | (elem!1 = z)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1632,plain,
% 0.51/0.78 (~b(s(s(elem!1)), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1631, 1551, 1477, 1518, 637, 1465, 1517, 1482, 99, 5])).
% 0.51/0.78 tff(1633,plain,
% 0.51/0.78 (r(s(s(elem!1)), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[843, 1632, 1481])).
% 0.51/0.78 tff(1634,plain,
% 0.51/0.78 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[704, 1633, 1477, 1434, 1475, 637])).
% 0.51/0.78 tff(1635,plain,
% 0.51/0.78 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[545, 1634, 1465])).
% 0.51/0.78 tff(1636,plain,
% 0.51/0.78 ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.51/0.78 inference(monotonicity,[status(thm)],[53])).
% 0.51/0.78 tff(1637,plain,
% 0.51/0.78 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1636])).
% 0.51/0.78 tff(1638,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(z)), introduced(assumption)).
% 0.51/0.78 tff(1639,plain,
% 0.51/0.78 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(z))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1638])).
% 0.51/0.78 tff(1640,plain,
% 0.51/0.78 (s(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.78 inference(symmetry,[status(thm)],[1436])).
% 0.51/0.78 tff(1641,plain,
% 0.51/0.78 (s(s(s(s(s(s(elem!1)))))) = z),
% 0.51/0.78 inference(transitivity,[status(thm)],[1640, 1639, 24])).
% 0.51/0.78 tff(1642,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[558, 1641])).
% 0.51/0.78 tff(1643,plain,(~(s(s(s(s(s(s(s(elem!1))))))) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1644,plain,
% 0.51/0.78 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1643, 1637])).
% 0.51/0.78 tff(1645,plain,
% 0.51/0.78 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1594, 1635, 1517])).
% 0.51/0.78 tff(1646,plain,
% 0.51/0.78 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[562, 1645])).
% 0.51/0.78 tff(1647,plain,
% 0.51/0.78 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1443, 500])).
% 0.51/0.78 tff(1648,plain,
% 0.51/0.78 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1460, 1647])).
% 0.51/0.78 tff(1649,plain,
% 0.51/0.78 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[179, 177])).
% 0.51/0.78 tff(1650,plain,
% 0.51/0.78 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[704, 254, 1649, 500, 643, 637])).
% 0.51/0.78 tff(1651,plain,
% 0.51/0.78 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[545, 1650, 221])).
% 0.51/0.78 tff(1652,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)), introduced(assumption)).
% 0.51/0.78 tff(1653,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)), introduced(assumption)).
% 0.51/0.78 tff(1654,plain,
% 0.51/0.78 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(elem!1))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1653])).
% 0.51/0.78 tff(1655,plain,
% 0.51/0.78 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.51/0.78 inference(transitivity,[status(thm)],[1640, 1654, 88])).
% 0.51/0.78 tff(1656,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[221, 1655])).
% 0.51/0.78 tff(1657,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1658,plain,
% 0.51/0.78 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1657, 221])).
% 0.51/0.78 tff(1659,plain,
% 0.51/0.78 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1594, 1651, 1032])).
% 0.51/0.78 tff(1660,plain,
% 0.51/0.78 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[562, 1659])).
% 0.51/0.78 tff(1661,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1662,plain,
% 0.51/0.78 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1663,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1662])).
% 0.51/0.78 tff(1664,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.78 inference(transitivity,[status(thm)],[1663, 1661])).
% 0.51/0.78 tff(1665,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1666,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1665, 1664])).
% 0.51/0.78 tff(1667,plain,
% 0.51/0.78 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1666, 371, 416, 1660])).
% 0.51/0.78 tff(1668,plain,
% 0.51/0.78 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[695, 1667, 500])).
% 0.51/0.78 tff(1669,assumption,(b(s(elem!1), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.51/0.78 tff(1670,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1671,plain,
% 0.51/0.78 (((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1672,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1671])).
% 0.51/0.78 tff(1673,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(transitivity,[status(thm)],[1672, 1670])).
% 0.51/0.78 tff(1674,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1675,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1674, 1673])).
% 0.51/0.78 tff(1676,plain,
% 0.51/0.78 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1675, 272, 643, 1669, 767])).
% 0.51/0.78 tff(1677,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), elem!1)), introduced(assumption)).
% 0.51/0.78 tff(1678,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1679,plain,
% 0.51/0.78 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1680,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.78 inference(monotonicity,[status(thm)],[1679])).
% 0.51/0.78 tff(1681,plain,
% 0.51/0.78 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(transitivity,[status(thm)],[1680, 1678])).
% 0.51/0.78 tff(1682,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1683,plain,
% 0.51/0.78 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1682, 1681])).
% 0.51/0.78 tff(1684,plain,
% 0.51/0.78 ($false),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1683, 272, 504, 1677, 767])).
% 0.51/0.78 tff(1685,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.78 tff(1686,plain,
% 0.51/0.78 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1685, 767, 504])).
% 0.51/0.78 tff(1687,plain,
% 0.51/0.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1688,plain,
% 0.51/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1689,plain,
% 0.51/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1688, 1687])).
% 0.51/0.78 tff(1690,plain,
% 0.51/0.78 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | b(s(s(s(s(s(s(s(elem!1))))))), elem!1) | r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1689, 139])).
% 0.51/0.78 tff(1691,plain,
% 0.51/0.78 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1690, 1686, 1652])).
% 0.51/0.78 tff(1692,plain,
% 0.51/0.78 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1693,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.51/0.78 inference(quant_inst,[status(thm)],[])).
% 0.51/0.78 tff(1694,plain,
% 0.51/0.78 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.51/0.78 inference(modus_ponens,[status(thm)],[1693, 1692])).
% 0.51/0.78 tff(1695,plain,
% 0.51/0.78 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.51/0.78 inference(unit_resolution,[status(thm)],[1694, 371, 637, 1691])).
% 0.51/0.78 tff(1696,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))), introduced(assumption)).
% 0.51/0.78 tff(1697,plain,
% 0.51/0.78 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.51/0.78 inference(rewrite,[status(thm)],[])).
% 0.51/0.78 tff(1698,plain,
% 0.51/0.78 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1699,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1698, 1697])).
% 0.51/0.79 tff(1700,plain,
% 0.51/0.79 ($false),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1699, 139, 1696, 1695, 1676])).
% 0.51/0.79 tff(1701,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.79 tff(1702,plain,
% 0.51/0.79 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1701, 1668, 643, 1658, 637, 1652, 1651])).
% 0.51/0.79 tff(1703,plain,
% 0.51/0.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1704,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1705,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1704, 1703])).
% 0.51/0.79 tff(1706,plain,
% 0.51/0.79 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1705, 139])).
% 0.51/0.79 tff(1707,plain,
% 0.51/0.79 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1706, 1702, 1648])).
% 0.51/0.79 tff(1708,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1709,plain,
% 0.51/0.79 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1710,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(monotonicity,[status(thm)],[1709])).
% 0.51/0.79 tff(1711,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(transitivity,[status(thm)],[1710, 1708])).
% 0.51/0.79 tff(1712,plain,
% 0.51/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1713,plain,
% 0.51/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1712, 1711])).
% 0.51/0.79 tff(1714,plain,
% 0.51/0.79 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1713, 272, 262, 1651])).
% 0.51/0.79 tff(1715,plain,
% 0.51/0.79 ((z = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = z)),
% 0.51/0.79 inference(commutativity,[status(thm)],[])).
% 0.51/0.79 tff(1716,plain,
% 0.51/0.79 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (z = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(symmetry,[status(thm)],[1715])).
% 0.51/0.79 tff(1717,plain,
% 0.51/0.79 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(z = s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(monotonicity,[status(thm)],[1716])).
% 0.51/0.79 tff(1718,plain,
% 0.51/0.79 (~(z = s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[558, 1717])).
% 0.51/0.79 tff(1719,plain,
% 0.51/0.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1720,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1721,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1720, 1719])).
% 0.51/0.79 tff(1722,plain,
% 0.51/0.79 ((z = s(s(s(s(s(s(elem!1))))))) | b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1721, 139])).
% 0.51/0.79 tff(1723,plain,
% 0.51/0.79 (b(z, s(s(s(s(s(s(elem!1))))))) | r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1722, 1718])).
% 0.51/0.79 tff(1724,plain,
% 0.51/0.79 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1723, 1714])).
% 0.51/0.79 tff(1725,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1726,plain,
% 0.51/0.79 (((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1727,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(monotonicity,[status(thm)],[1726])).
% 0.51/0.79 tff(1728,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(transitivity,[status(thm)],[1727, 1725])).
% 0.51/0.79 tff(1729,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1730,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1729, 1728])).
% 0.51/0.79 tff(1731,plain,
% 0.51/0.79 (~r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1730, 371, 1724, 1707])).
% 0.51/0.79 tff(1732,plain,
% 0.51/0.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1733,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1734,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = z) | b(s(s(s(s(s(s(s(elem!1))))))), z) | r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1733, 1732])).
% 0.51/0.79 tff(1735,plain,
% 0.51/0.79 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1734, 139, 170, 1731])).
% 0.51/0.79 tff(1736,plain,
% 0.51/0.79 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[502, 500])).
% 0.51/0.79 tff(1737,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1738,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1739,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1738, 1737])).
% 0.51/0.79 tff(1740,plain,
% 0.51/0.79 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1739, 371, 416, 1660])).
% 0.51/0.79 tff(1741,plain,
% 0.51/0.79 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[527, 1740, 1736])).
% 0.51/0.79 tff(1742,plain,
% 0.51/0.79 (~r(s(s(elem!1)), s(elem!1))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[655, 371, 254, 637])).
% 0.51/0.79 tff(1743,plain,
% 0.51/0.79 (b(s(s(elem!1)), s(elem!1))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[660, 1742, 244])).
% 0.51/0.79 tff(1744,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1745,plain,
% 0.51/0.79 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1746,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(monotonicity,[status(thm)],[1745])).
% 0.51/0.79 tff(1747,plain,
% 0.51/0.79 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(transitivity,[status(thm)],[1746, 1744])).
% 0.51/0.79 tff(1748,plain,
% 0.51/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1749,plain,
% 0.51/0.79 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 0.51/0.79 tff(1750,plain,
% 0.51/0.79 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1749, 272, 1743, 1651, 1741])).
% 0.51/0.79 tff(1751,plain,
% 0.51/0.79 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[963, 139, 177, 1750])).
% 0.51/0.79 tff(1752,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.51/0.79 tff(1753,assumption,(r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 0.51/0.79 tff(1754,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1755,plain,
% 0.51/0.79 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1756,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.51/0.79 inference(monotonicity,[status(thm)],[1755])).
% 0.51/0.79 tff(1757,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(transitivity,[status(thm)],[1756, 1754])).
% 0.51/0.79 tff(1758,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1759,plain,
% 0.51/0.79 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1758, 1757])).
% 0.51/0.79 tff(1760,plain,
% 0.51/0.79 ($false),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1759, 371, 1753, 1752, 944])).
% 0.51/0.79 tff(1761,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.51/0.79 tff(1762,plain,
% 0.51/0.79 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1761, 1707, 1751])).
% 0.51/0.79 tff(1763,plain,
% 0.51/0.79 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1764,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.51/0.79 inference(quant_inst,[status(thm)],[])).
% 0.51/0.79 tff(1765,plain,
% 0.51/0.79 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(modus_ponens,[status(thm)],[1764, 1763])).
% 0.51/0.79 tff(1766,plain,
% 0.51/0.79 ((s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1765, 139])).
% 0.51/0.79 tff(1767,plain,
% 0.51/0.79 (b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.51/0.79 inference(unit_resolution,[status(thm)],[1766, 1762, 1647])).
% 0.51/0.79 tff(1768,assumption,(r(s(s(s(s(s(s(elem!1)))))), z)), introduced(assumption)).
% 0.51/0.79 tff(1769,plain,
% 0.51/0.79 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.51/0.79 inference(rewrite,[status(thm)],[])).
% 0.51/0.79 tff(1770,plain,
% 0.51/0.79 (((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1771,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1770])).
% 0.60/0.80 tff(1772,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1771, 1769])).
% 0.60/0.80 tff(1773,plain,
% 0.60/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1774,plain,
% 0.60/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1773, 1772])).
% 0.60/0.80 tff(1775,plain,
% 0.60/0.80 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1774, 371, 1019, 1768])).
% 0.60/0.80 tff(1776,plain,
% 0.60/0.80 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[963, 139, 177, 1775])).
% 0.60/0.80 tff(1777,plain,
% 0.60/0.80 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1739, 371, 416, 1768])).
% 0.60/0.80 tff(1778,plain,
% 0.60/0.80 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[527, 1777, 513])).
% 0.60/0.80 tff(1779,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1780,plain,
% 0.60/0.80 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1781,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1780])).
% 0.60/0.80 tff(1782,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1781, 1779])).
% 0.60/0.80 tff(1783,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1784,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1783, 1782])).
% 0.60/0.80 tff(1785,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1784, 272, 717, 1778, 1776])).
% 0.60/0.80 tff(1786,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1787,plain,
% 0.60/0.80 (~r(s(s(elem!1)), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1786, 1743, 177, 416, 1736, 1660])).
% 0.60/0.80 tff(1788,plain,
% 0.60/0.80 (b(s(s(elem!1)), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[453, 1787])).
% 0.60/0.80 tff(1789,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1790,plain,
% 0.60/0.80 (((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1791,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1790])).
% 0.60/0.80 tff(1792,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1791, 1789])).
% 0.60/0.80 tff(1793,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1794,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1793, 1792])).
% 0.60/0.80 tff(1795,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1794, 272, 1788, 1767, 1735])).
% 0.60/0.80 tff(1796,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), z)) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1797,plain,
% 0.60/0.80 (~r(s(elem!1), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1796, 1633, 637, 1644, 1476, 1475, 1434, 99, 1551, 1517, 1465])).
% 0.60/0.80 tff(1798,plain,
% 0.60/0.80 (b(s(elem!1), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[414, 1797])).
% 0.60/0.80 tff(1799,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1501, 272, 399, 1030, 643])).
% 0.60/0.80 tff(1800,plain,((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1801,plain,
% 0.60/0.80 (~b(s(s(elem!1)), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1800, 1798, 1475])).
% 0.60/0.80 tff(1802,plain,
% 0.60/0.80 (r(s(s(elem!1)), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[453, 1801])).
% 0.60/0.80 tff(1803,plain,
% 0.60/0.80 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1774, 371, 1802, 1646])).
% 0.60/0.80 tff(1804,plain,
% 0.60/0.80 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[963, 139, 1476, 1803])).
% 0.60/0.80 tff(1805,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.80 tff(1806,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1807,plain,
% 0.60/0.80 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1808,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1807])).
% 0.60/0.80 tff(1809,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1808, 1806])).
% 0.60/0.80 tff(1810,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1811,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 0.60/0.80 tff(1812,plain,
% 0.60/0.80 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1811, 272, 767, 1805])).
% 0.60/0.80 tff(1813,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1814,plain,
% 0.60/0.80 (((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1815,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1814])).
% 0.60/0.80 tff(1816,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1815, 1813])).
% 0.60/0.80 tff(1817,plain,
% 0.60/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1818,plain,
% 0.60/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1817, 1816])).
% 0.60/0.80 tff(1819,plain,
% 0.60/0.80 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1818, 371, 254, 1691])).
% 0.60/0.80 tff(1820,plain,
% 0.60/0.80 ($false),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1766, 1819, 1812, 1457])).
% 0.60/0.80 tff(1821,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.80 tff(1822,plain,
% 0.60/0.80 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1821, 1804, 1444, 1633, 1644, 1635])).
% 0.60/0.80 tff(1823,plain,
% 0.60/0.80 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1706, 1822, 1461])).
% 0.60/0.80 tff(1824,plain,
% 0.60/0.80 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1713, 272, 1551, 1635])).
% 0.60/0.80 tff(1825,plain,
% 0.60/0.80 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1723, 1824])).
% 0.60/0.80 tff(1826,plain,
% 0.60/0.80 (~r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1730, 371, 1825, 1823])).
% 0.60/0.80 tff(1827,plain,
% 0.60/0.80 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1734, 139, 170, 1826])).
% 0.60/0.80 tff(1828,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1829,plain,
% 0.60/0.80 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1830,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[1829])).
% 0.60/0.80 tff(1831,plain,
% 0.60/0.80 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.80 inference(transitivity,[status(thm)],[1830, 1828])).
% 0.60/0.80 tff(1832,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(1833,plain,
% 0.60/0.80 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[1832, 1831])).
% 0.60/0.80 tff(1834,plain,
% 0.60/0.80 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1833, 272, 1798, 1827])).
% 0.60/0.80 tff(1835,plain,
% 0.60/0.80 (~r(s(s(elem!1)), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[655, 371, 1633, 637])).
% 0.60/0.80 tff(1836,plain,
% 0.60/0.80 (b(s(s(elem!1)), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[660, 1835, 99])).
% 0.60/0.80 tff(1837,plain,
% 0.60/0.80 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1181, 371, 1802, 1646])).
% 0.60/0.80 tff(1838,plain,
% 0.60/0.80 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[611, 139, 1477, 1837])).
% 0.60/0.80 tff(1839,plain,
% 0.60/0.80 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[1618, 1838, 1836])).
% 0.60/0.80 tff(1840,plain,
% 0.60/0.80 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[527, 1839, 1518])).
% 0.60/0.80 tff(1841,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))), introduced(assumption)).
% 0.60/0.80 tff(1842,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(elem!1))), introduced(assumption)).
% 0.60/0.80 tff(1843,plain,
% 0.60/0.80 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(1844,plain,
% 0.60/0.80 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1845,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1844, 1843])).
% 0.60/0.81 tff(1846,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1845, 371, 1842, 1752, 1841])).
% 0.60/0.81 tff(1847,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1848,plain,
% 0.60/0.81 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1847, 1840, 1823])).
% 0.60/0.81 tff(1849,plain,
% 0.60/0.81 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1657, 1465])).
% 0.60/0.81 tff(1850,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1699, 139, 1849, 1848, 1834])).
% 0.60/0.81 tff(1851,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(elem!1), elem!1)) | (elem!1 = z) | (~(s(z) = elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1852,plain,
% 0.60/0.81 (~r(elem!1, s(s(s(z))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1851, 1426, 260, 144, 1425])).
% 0.60/0.81 tff(1853,plain,
% 0.60/0.81 (((~![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)))))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1854,plain,
% 0.60/0.81 ((~![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)))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1855,plain,
% 0.60/0.81 ((~![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))))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1854, 1853])).
% 0.60/0.81 tff(1856,plain,
% 0.60/0.81 ((elem!1 = s(s(s(z)))) | b(elem!1, s(s(s(z)))) | r(elem!1, s(s(s(z))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1855, 139])).
% 0.60/0.81 tff(1857,plain,
% 0.60/0.81 (b(elem!1, s(s(s(z))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1856, 1852, 197])).
% 0.60/0.81 tff(1858,plain,
% 0.60/0.81 (b(elem!1, s(s(elem!1)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1857, 183])).
% 0.60/0.81 tff(1859,plain,
% 0.60/0.81 (b(s(s(z)), elem!1) <=> b(s(elem!1), elem!1)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[181])).
% 0.60/0.81 tff(1860,plain,
% 0.60/0.81 ((~b(s(s(z)), elem!1)) <=> (~b(s(elem!1), elem!1))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1859])).
% 0.60/0.81 tff(1861,plain,
% 0.60/0.81 (~b(s(elem!1), elem!1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[202, 1860])).
% 0.60/0.81 tff(1862,plain,
% 0.60/0.81 ((elem!1 = s(z)) <=> (s(z) = elem!1)),
% 0.60/0.81 inference(commutativity,[status(thm)],[])).
% 0.60/0.81 tff(1863,plain,
% 0.60/0.81 ((s(z) = elem!1) <=> (elem!1 = s(z))),
% 0.60/0.81 inference(symmetry,[status(thm)],[1862])).
% 0.60/0.81 tff(1864,plain,
% 0.60/0.81 (elem!1 = s(z)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[53, 1863])).
% 0.60/0.81 tff(1865,plain,
% 0.60/0.81 (r(z, s(z)) <=> r(z, elem!1)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[53])).
% 0.60/0.81 tff(1866,plain,
% 0.60/0.81 (r(z, elem!1) <=> r(z, s(z))),
% 0.60/0.81 inference(symmetry,[status(thm)],[1865])).
% 0.60/0.81 tff(1867,assumption,(~b(elem!1, z)), introduced(assumption)).
% 0.60/0.81 tff(1868,plain,
% 0.60/0.81 (b(s(s(z)), z) <=> b(s(elem!1), z)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[54])).
% 0.60/0.81 tff(1869,plain,
% 0.60/0.81 (r(elem!1, z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[997, 1867, 260])).
% 0.60/0.81 tff(1870,plain,
% 0.60/0.81 (~r(s(s(z)), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[981, 1869, 434])).
% 0.60/0.81 tff(1871,plain,
% 0.60/0.81 (b(s(s(z)), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[462, 1870])).
% 0.60/0.81 tff(1872,plain,
% 0.60/0.81 (b(s(elem!1), z)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1871, 1868])).
% 0.60/0.81 tff(1873,plain,
% 0.60/0.81 (b(s(elem!1), z) <=> b(elem!1, z)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[238])).
% 0.60/0.81 tff(1874,plain,
% 0.60/0.81 (b(elem!1, z) <=> b(s(elem!1), z)),
% 0.60/0.81 inference(symmetry,[status(thm)],[1873])).
% 0.60/0.81 tff(1875,plain,
% 0.60/0.81 ((~b(elem!1, z)) <=> (~b(s(elem!1), z))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1874])).
% 0.60/0.81 tff(1876,plain,
% 0.60/0.81 (~b(s(elem!1), z)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1867, 1875])).
% 0.60/0.81 tff(1877,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[399, 1876])).
% 0.60/0.81 tff(1878,plain,((~(s(elem!1) = elem!1)) | (~b(s(elem!1), z)) | b(elem!1, z)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1879,plain,
% 0.60/0.81 (~(s(elem!1) = elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1878, 399, 1867])).
% 0.60/0.81 tff(1880,plain,
% 0.60/0.81 (r(s(elem!1), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[618, 1879, 52])).
% 0.60/0.81 tff(1881,plain,
% 0.60/0.81 (s(z) = s(elem!1)),
% 0.60/0.81 inference(symmetry,[status(thm)],[25])).
% 0.60/0.81 tff(1882,plain,
% 0.60/0.81 (inj_0(s(z)) = inj_0(s(elem!1))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1881])).
% 0.60/0.81 tff(1883,plain,
% 0.60/0.81 (z = inj_0(s(z))),
% 0.60/0.81 inference(symmetry,[status(thm)],[24])).
% 0.60/0.81 tff(1884,plain,
% 0.60/0.81 (z = elem!1),
% 0.60/0.81 inference(transitivity,[status(thm)],[1883, 1882, 88])).
% 0.60/0.81 tff(1885,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1362, 1884])).
% 0.60/0.81 tff(1886,plain,((~(s(elem!1) = s(z))) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1887,plain,
% 0.60/0.81 (z = elem!1),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1886, 25])).
% 0.60/0.81 tff(1888,plain,
% 0.60/0.81 (b(s(z), z) <=> b(s(z), elem!1)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1887])).
% 0.60/0.81 tff(1889,plain,
% 0.60/0.81 (b(s(z), elem!1) <=> b(s(z), z)),
% 0.60/0.81 inference(symmetry,[status(thm)],[1888])).
% 0.60/0.81 tff(1890,plain,
% 0.60/0.81 ((~b(s(z), elem!1)) <=> (~b(s(z), z))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1889])).
% 0.60/0.81 tff(1891,plain,
% 0.60/0.81 (~b(s(z), z)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[129, 1890])).
% 0.60/0.81 tff(1892,plain,
% 0.60/0.81 (b(s(elem!1), z) <=> b(s(z), z)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[25])).
% 0.60/0.81 tff(1893,plain,
% 0.60/0.81 (b(s(z), z)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[399, 1892])).
% 0.60/0.81 tff(1894,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1893, 1891])).
% 0.60/0.81 tff(1895,plain,((~(s(elem!1) = s(z))) | b(s(z), elem!1) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1896,plain,
% 0.60/0.81 (~(s(elem!1) = s(z))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1895, 399, 129])).
% 0.60/0.81 tff(1897,plain,
% 0.60/0.81 (~(elem!1 = z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[13, 1896])).
% 0.60/0.81 tff(1898,plain,
% 0.60/0.81 (r(elem!1, z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[997, 1897, 1867])).
% 0.60/0.81 tff(1899,plain,
% 0.60/0.81 (~r(s(elem!1), s(z))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1106, 1101, 637])).
% 0.60/0.81 tff(1900,plain,
% 0.60/0.81 (b(s(elem!1), s(z))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[324, 1899, 11])).
% 0.60/0.81 tff(1901,plain,
% 0.60/0.81 (~b(s(z), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1316, 1900, 399])).
% 0.60/0.81 tff(1902,plain,
% 0.60/0.81 (r(s(z), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[289, 1901])).
% 0.60/0.81 tff(1903,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1904,plain,
% 0.60/0.81 (((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1905,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1904])).
% 0.60/0.81 tff(1906,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1905, 1903])).
% 0.60/0.81 tff(1907,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(z), z)) | (~r(s(z), elem!1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1908,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1907, 1906])).
% 0.60/0.81 tff(1909,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1908, 371, 972, 1101, 1902])).
% 0.60/0.81 tff(1910,plain,((~r(s(z), elem!1)) | (~r(elem!1, z)) | (~b(s(elem!1), z)) | (s(elem!1) = s(z)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1911,plain,
% 0.60/0.81 (~r(s(z), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1910, 1898, 399, 1896, 1880])).
% 0.60/0.81 tff(1912,plain,
% 0.60/0.81 (s(z) = elem!1),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[143, 1911, 129])).
% 0.60/0.81 tff(1913,plain,
% 0.60/0.81 ((s(z) = s(s(elem!1))) <=> (elem!1 = s(s(elem!1)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1912])).
% 0.60/0.81 tff(1914,plain,
% 0.60/0.81 ((s(z) = s(s(elem!1))) <=> (s(s(elem!1)) = elem!1)),
% 0.60/0.81 inference(transitivity,[status(thm)],[1913, 77])).
% 0.60/0.81 tff(1915,plain,
% 0.60/0.81 ((~(s(z) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = elem!1))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1914])).
% 0.60/0.81 tff(1916,plain,
% 0.60/0.81 (~(s(s(elem!1)) = elem!1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[857, 1915])).
% 0.60/0.81 tff(1917,plain,
% 0.60/0.81 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1912])).
% 0.60/0.81 tff(1918,plain,
% 0.60/0.81 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.60/0.81 inference(transitivity,[status(thm)],[1917, 127])).
% 0.60/0.81 tff(1919,plain,
% 0.60/0.81 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1918])).
% 0.60/0.81 tff(1920,plain,
% 0.60/0.81 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[155, 1919])).
% 0.60/0.81 tff(1921,plain,
% 0.60/0.81 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1433, 1912])).
% 0.60/0.81 tff(1922,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1923,plain,
% 0.60/0.81 (((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1924,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1923])).
% 0.60/0.81 tff(1925,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1924, 1922])).
% 0.60/0.81 tff(1926,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1927,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), z))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 0.60/0.81 tff(1928,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1927, 371, 972, 552, 1768])).
% 0.60/0.81 tff(1929,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(elem!1, z)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1930,plain,
% 0.60/0.81 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1929, 552, 972])).
% 0.60/0.81 tff(1931,plain,
% 0.60/0.81 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[562, 1930])).
% 0.60/0.81 tff(1932,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[935, 272, 399, 696, 1931])).
% 0.60/0.81 tff(1933,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1934,plain,
% 0.60/0.81 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1933, 399, 1898, 1921, 1880])).
% 0.60/0.81 tff(1935,plain,
% 0.60/0.81 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[545, 1934, 1920])).
% 0.60/0.81 tff(1936,assumption,(~r(z, elem!1)), introduced(assumption)).
% 0.60/0.81 tff(1937,plain,
% 0.60/0.81 (~(z = elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[7, 1897])).
% 0.60/0.81 tff(1938,plain,
% 0.60/0.81 (b(z, elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[432, 1937, 1936])).
% 0.60/0.81 tff(1939,plain,
% 0.60/0.81 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[669, 272, 1938, 1935])).
% 0.60/0.81 tff(1940,plain,
% 0.60/0.81 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[562, 1939])).
% 0.60/0.81 tff(1941,plain,
% 0.60/0.81 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[172, 1912])).
% 0.60/0.81 tff(1942,plain,
% 0.60/0.81 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[179, 1941])).
% 0.60/0.81 tff(1943,plain,
% 0.60/0.81 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1181, 371, 1019, 1768])).
% 0.60/0.81 tff(1944,plain,
% 0.60/0.81 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[611, 139, 662, 1943])).
% 0.60/0.81 tff(1945,plain,
% 0.60/0.81 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1946,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1947,plain,
% 0.60/0.81 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), elem!1))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1946, 1945])).
% 0.60/0.81 tff(1948,plain,
% 0.60/0.81 (~r(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1947, 371, 972, 1019])).
% 0.60/0.81 tff(1949,plain,
% 0.60/0.81 (b(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[843, 1948, 233])).
% 0.60/0.81 tff(1950,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1173, 272, 1949, 504, 1944])).
% 0.60/0.81 tff(1951,plain,((~r(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (s(s(elem!1)) = elem!1) | (~r(s(s(s(s(s(s(elem!1)))))), z)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1952,plain,
% 0.60/0.81 (~r(s(s(elem!1)), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1951, 1935, 1942, 1916, 1940, 1898])).
% 0.60/0.81 tff(1953,plain,
% 0.60/0.81 (b(s(s(elem!1)), z)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[453, 1952])).
% 0.60/0.81 tff(1954,plain,
% 0.60/0.81 (~b(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1094, 1938, 1953])).
% 0.60/0.81 tff(1955,plain,
% 0.60/0.81 (r(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[843, 1954, 1916])).
% 0.60/0.81 tff(1956,plain,
% 0.60/0.81 (~(elem!1 = s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1558, 1879])).
% 0.60/0.81 tff(1957,plain,
% 0.60/0.81 (~(s(s(elem!1)) = s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[93, 1956])).
% 0.60/0.81 tff(1958,plain,
% 0.60/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1959,plain,
% 0.60/0.81 (((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(1960,plain,
% 0.60/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[1959])).
% 0.60/0.81 tff(1961,plain,
% 0.60/0.81 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[1960, 1958])).
% 0.60/0.81 tff(1962,plain,
% 0.60/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(1963,plain,
% 0.60/0.81 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), z))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1962, 1961])).
% 0.60/0.81 tff(1964,plain,
% 0.60/0.81 (~b(s(s(elem!1)), s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1963, 272, 399, 1953])).
% 0.60/0.81 tff(1965,plain,
% 0.60/0.81 (r(s(s(elem!1)), s(elem!1))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[660, 1964, 1957])).
% 0.60/0.81 tff(1966,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[655, 371, 1965, 1955, 1880])).
% 0.60/0.81 tff(1967,plain,((~b(s(elem!1), z)) | b(s(z), elem!1) | r(z, elem!1) | b(elem!1, z) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(1968,plain,
% 0.60/0.81 (r(z, elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1967, 1872, 129, 1867, 52])).
% 0.60/0.81 tff(1969,plain,
% 0.60/0.81 (r(z, s(z))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[1968, 1866])).
% 0.60/0.81 tff(1970,plain,
% 0.60/0.81 (r(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[53])).
% 0.60/0.81 tff(1971,plain,
% 0.60/0.81 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.81 inference(symmetry,[status(thm)],[1970])).
% 0.60/0.81 tff(1972,plain,
% 0.60/0.81 (r(s(s(z)), elem!1) <=> r(s(elem!1), elem!1)),
% 0.60/0.81 inference(monotonicity,[status(thm)],[54])).
% 0.60/0.81 tff(1973,plain,
% 0.60/0.81 (r(s(elem!1), elem!1)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[434, 1972])).
% 0.60/0.81 tff(1974,plain,
% 0.60/0.81 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[1933, 1872, 1973, 1434, 1869])).
% 0.60/0.81 tff(1975,plain,
% 0.60/0.81 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[545, 1974, 1465])).
% 0.60/0.81 tff(1976,plain,
% 0.60/0.81 (~r(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[471, 1968, 434, 203])).
% 0.60/0.81 tff(1977,plain,
% 0.60/0.81 (b(s(s(elem!1)), elem!1)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[843, 1976, 1481])).
% 0.60/0.81 tff(1978,plain,
% 0.60/0.81 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[959, 272, 1977, 1975])).
% 0.60/0.81 tff(1979,plain,
% 0.60/0.81 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[963, 139, 1476, 1978])).
% 0.60/0.81 tff(1980,plain,
% 0.60/0.81 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1460, 1457])).
% 0.60/0.82 tff(1981,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1685, 1677, 504])).
% 0.60/0.82 tff(1982,plain,
% 0.60/0.82 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1706, 1981, 1980])).
% 0.60/0.82 tff(1983,assumption,(b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 0.60/0.82 tff(1984,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1985,plain,
% 0.60/0.82 (((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(1986,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[1985])).
% 0.60/0.82 tff(1987,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[1986, 1984])).
% 0.60/0.82 tff(1988,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(1989,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1988, 1987])).
% 0.60/0.82 tff(1990,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1989, 272, 864, 1983, 1677])).
% 0.60/0.82 tff(1991,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1992,plain,
% 0.60/0.82 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1991, 1677, 864])).
% 0.60/0.82 tff(1993,plain,
% 0.60/0.82 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1766, 1992, 1457])).
% 0.60/0.82 tff(1994,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1761, 1993, 1982, 944])).
% 0.60/0.82 tff(1995,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(1996,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1995, 1979, 1444, 1977, 1975])).
% 0.60/0.82 tff(1997,plain,
% 0.60/0.82 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1690, 1996, 1644])).
% 0.60/0.82 tff(1998,plain,
% 0.60/0.82 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1997, 1971])).
% 0.60/0.82 tff(1999,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(z))), introduced(assumption)).
% 0.60/0.82 tff(2000,plain,
% 0.60/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2001,plain,
% 0.60/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(2002,plain,
% 0.60/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2001, 2000])).
% 0.60/0.82 tff(2003,plain,
% 0.60/0.82 (~r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2002, 371, 417, 1999])).
% 0.60/0.82 tff(2004,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1734, 139, 170, 2003])).
% 0.60/0.82 tff(2005,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))), introduced(assumption)).
% 0.60/0.82 tff(2006,assumption,(elem!1 = s(z)), introduced(assumption)).
% 0.60/0.82 tff(2007,plain,
% 0.60/0.82 (r(z, elem!1) <=> r(z, s(z))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2006])).
% 0.60/0.82 tff(2008,plain,
% 0.60/0.82 (r(z, s(z)) <=> r(z, elem!1)),
% 0.60/0.82 inference(symmetry,[status(thm)],[2007])).
% 0.60/0.82 tff(2009,plain,
% 0.60/0.82 (r(z, elem!1)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[417, 2008])).
% 0.60/0.82 tff(2010,plain,
% 0.60/0.82 (~r(z, s(s(z)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1063, 2009, 434])).
% 0.60/0.82 tff(2011,plain,
% 0.60/0.82 (b(z, s(s(z)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1073, 2010])).
% 0.60/0.82 tff(2012,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2013,plain,
% 0.60/0.82 (((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2014,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2013])).
% 0.60/0.82 tff(2015,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[2014, 2012])).
% 0.60/0.82 tff(2016,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(2017,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2016, 2015])).
% 0.60/0.82 tff(2018,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2017, 272, 2011, 2005, 2004])).
% 0.60/0.82 tff(2019,plain,((~r(z, s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2020,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2019, 1998, 1864, 1969, 434])).
% 0.60/0.82 tff(2021,plain,
% 0.60/0.82 (s(elem!1) = s(s(z))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2006])).
% 0.60/0.82 tff(2022,plain,
% 0.60/0.82 (s(s(z)) = s(elem!1)),
% 0.60/0.82 inference(symmetry,[status(thm)],[2021])).
% 0.60/0.82 tff(2023,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2022])).
% 0.60/0.82 tff(2024,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.60/0.82 inference(symmetry,[status(thm)],[2023])).
% 0.60/0.82 tff(2025,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))), introduced(assumption)).
% 0.60/0.82 tff(2026,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2025, 2024])).
% 0.60/0.82 tff(2027,assumption,(~b(s(s(s(s(s(s(s(elem!1))))))), s(s(z)))), introduced(assumption)).
% 0.60/0.82 tff(2028,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2027, 2026])).
% 0.60/0.82 tff(2029,plain,(b(s(s(s(s(s(s(s(elem!1))))))), s(s(z))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~(elem!1 = s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2030,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2029, 2020, 1864])).
% 0.60/0.82 tff(2031,plain,
% 0.60/0.82 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1694, 371, 1973, 1997])).
% 0.60/0.82 tff(2032,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1699, 139, 1849, 2031, 2030])).
% 0.60/0.82 tff(2033,plain,(b(elem!1, z) | (~r(s(s(z)), elem!1)) | (~(s(z) = elem!1)) | (s(s(z)) = s(s(elem!1))) | b(s(z), elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2034,plain,
% 0.60/0.82 (b(elem!1, z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2033, 144, 1424, 203, 129, 1861])).
% 0.60/0.82 tff(2035,plain,
% 0.60/0.82 (~b(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1040, 1032, 1031])).
% 0.60/0.82 tff(2036,plain,
% 0.60/0.82 (r(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[453, 2035])).
% 0.60/0.82 tff(2037,plain,
% 0.60/0.82 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1181, 371, 2036, 1596])).
% 0.60/0.82 tff(2038,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[611, 139, 662, 2037])).
% 0.60/0.82 tff(2039,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2040,plain,
% 0.60/0.82 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2041,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2040])).
% 0.60/0.82 tff(2042,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[2041, 2039])).
% 0.60/0.82 tff(2043,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(2044,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2043, 2042])).
% 0.60/0.82 tff(2045,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2044, 272, 1032, 1031, 504, 2038])).
% 0.60/0.82 tff(2046,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(elem!1)))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2047,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2046, 2034, 1858, 180])).
% 0.60/0.82 tff(2048,plain,
% 0.60/0.82 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[545, 2047, 156])).
% 0.60/0.82 tff(2049,plain,
% 0.60/0.82 ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.82 inference(monotonicity,[status(thm)],[144])).
% 0.60/0.82 tff(2050,plain,
% 0.60/0.82 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2049])).
% 0.60/0.82 tff(2051,plain,
% 0.60/0.82 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1643, 2050])).
% 0.60/0.82 tff(2052,plain,
% 0.60/0.82 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[144])).
% 0.60/0.82 tff(2053,plain,
% 0.60/0.82 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.60/0.82 inference(symmetry,[status(thm)],[2052])).
% 0.60/0.82 tff(2054,plain,
% 0.60/0.82 (b(elem!1, s(s(s(z)))) <=> b(s(z), s(s(elem!1)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[183, 2053])).
% 0.60/0.82 tff(2055,plain,
% 0.60/0.82 (b(s(z), s(s(elem!1)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[1857, 2054])).
% 0.60/0.82 tff(2056,plain,
% 0.60/0.82 (~(elem!1 = s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[75, 144])).
% 0.60/0.82 tff(2057,plain,
% 0.60/0.82 (~(s(s(elem!1)) = s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[98, 2056])).
% 0.60/0.82 tff(2058,plain,
% 0.60/0.82 (~(s(elem!1) = s(z))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1886, 1362])).
% 0.60/0.82 tff(2059,assumption,(b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.60/0.82 tff(2060,plain,
% 0.60/0.82 (b(s(z), elem!1) <=> b(s(z), s(s(elem!1)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[64])).
% 0.60/0.82 tff(2061,plain,
% 0.60/0.82 (b(s(z), s(s(elem!1))) <=> b(s(z), elem!1)),
% 0.60/0.82 inference(symmetry,[status(thm)],[2060])).
% 0.60/0.82 tff(2062,plain,
% 0.60/0.82 (b(s(z), elem!1)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2059, 2061])).
% 0.60/0.82 tff(2063,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[129, 2062])).
% 0.60/0.82 tff(2064,plain,((~(elem!1 = s(s(elem!1)))) | b(s(z), elem!1) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2065,plain,
% 0.60/0.82 (~(elem!1 = s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2064, 129, 2059])).
% 0.60/0.82 tff(2066,plain,
% 0.60/0.82 (~r(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1052, 902, 637])).
% 0.60/0.82 tff(2067,plain,
% 0.60/0.82 (b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1045, 2066, 96])).
% 0.60/0.82 tff(2068,plain,
% 0.60/0.82 (~b(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1040, 2067, 1032])).
% 0.60/0.82 tff(2069,plain,
% 0.60/0.82 (r(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[453, 2068])).
% 0.60/0.82 tff(2070,plain,
% 0.60/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2071,plain,
% 0.60/0.82 (((~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), s(s(elem!1))))) <=> ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2072,plain,
% 0.60/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2071])).
% 0.60/0.82 tff(2073,plain,
% 0.60/0.82 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[2072, 2070])).
% 0.60/0.82 tff(2074,plain,
% 0.60/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(2075,plain,
% 0.60/0.82 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(s(s(elem!1)), z)) | (~r(s(elem!1), z))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2074, 2073])).
% 0.60/0.82 tff(2076,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2075, 371, 416, 2069, 902])).
% 0.60/0.82 tff(2077,plain,((~r(s(elem!1), s(s(elem!1)))) | (~r(s(elem!1), z)) | (~b(elem!1, z)) | (elem!1 = s(s(elem!1))) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(2078,plain,
% 0.60/0.82 (~r(s(elem!1), s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2077, 637, 1032, 2065, 416])).
% 0.60/0.82 tff(2079,plain,
% 0.60/0.82 (b(s(elem!1), s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[635, 2078, 1347])).
% 0.60/0.82 tff(2080,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2081,plain,
% 0.60/0.82 (((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(2082,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2081])).
% 0.60/0.82 tff(2083,plain,
% 0.60/0.82 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.60/0.82 inference(transitivity,[status(thm)],[2082, 2080])).
% 0.60/0.82 tff(2084,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z))))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(2085,plain,
% 0.60/0.82 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(elem!1), s(z)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2084, 2083])).
% 0.60/0.82 tff(2086,plain,
% 0.60/0.82 (~b(s(elem!1), s(z))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2085, 272, 2059, 2079])).
% 0.60/0.82 tff(2087,plain,
% 0.60/0.82 (r(s(elem!1), s(z))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[324, 2086, 2058])).
% 0.60/0.82 tff(2088,plain,
% 0.60/0.82 (~r(s(z), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1106, 2087, 637])).
% 0.60/0.82 tff(2089,plain,
% 0.60/0.82 (s(z) = elem!1),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[143, 2088, 129])).
% 0.60/0.82 tff(2090,plain,
% 0.60/0.82 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[2089])).
% 0.60/0.82 tff(2091,plain,
% 0.60/0.82 (b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2059, 2090])).
% 0.60/0.82 tff(2092,plain,
% 0.60/0.82 (~b(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1040, 2091, 1032])).
% 0.60/0.82 tff(2093,plain,
% 0.60/0.82 (r(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[453, 2092])).
% 0.60/0.82 tff(2094,plain,
% 0.60/0.82 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1433, 2089])).
% 0.60/0.82 tff(2095,plain,
% 0.60/0.82 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[502, 2094])).
% 0.60/0.82 tff(2096,plain,
% 0.60/0.82 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[172, 2089])).
% 0.60/0.82 tff(2097,plain,
% 0.60/0.82 (~r(s(s(elem!1)), s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1222, 2093, 416])).
% 0.60/0.82 tff(2098,plain,
% 0.60/0.82 (b(s(s(elem!1)), s(elem!1))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[660, 2097, 244])).
% 0.60/0.82 tff(2099,plain,
% 0.60/0.82 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1786, 2098, 2096, 2095, 2093, 416])).
% 0.60/0.82 tff(2100,plain,
% 0.60/0.82 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[562, 2099])).
% 0.60/0.82 tff(2101,plain,
% 0.60/0.82 (~r(z, elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[828, 637, 416])).
% 0.60/0.82 tff(2102,plain,
% 0.60/0.82 (b(z, elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[432, 2101, 1362])).
% 0.60/0.82 tff(2103,plain,
% 0.60/0.82 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1594, 2100, 1032])).
% 0.60/0.82 tff(2104,assumption,(~b(s(s(s(s(s(s(elem!1)))))), elem!1)), introduced(assumption)).
% 0.60/0.82 tff(2105,plain,
% 0.60/0.82 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[545, 1465, 2104])).
% 0.60/0.82 tff(2106,plain,
% 0.60/0.82 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[690, 371, 637, 2105])).
% 0.60/0.82 tff(2107,plain,
% 0.60/0.82 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[695, 2106, 1434])).
% 0.60/0.82 tff(2108,plain,
% 0.60/0.82 (b(s(z), s(s(elem!1))) <=> b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[53])).
% 0.60/0.82 tff(2109,plain,
% 0.60/0.82 (b(elem!1, s(s(elem!1)))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[2059, 2108])).
% 0.60/0.82 tff(2110,plain,
% 0.60/0.82 (~b(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[1040, 2109, 1032])).
% 0.60/0.82 tff(2111,plain,
% 0.60/0.82 (r(s(s(elem!1)), z)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[453, 2110])).
% 0.60/0.82 tff(2112,plain,
% 0.60/0.82 (~r(s(elem!1), s(s(elem!1)))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[2075, 371, 416, 2111])).
% 0.60/0.82 tff(2113,plain,
% 0.60/0.83 (b(s(elem!1), s(s(elem!1)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[635, 2112, 1347])).
% 0.60/0.83 tff(2114,plain,
% 0.60/0.83 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1155, 371, 637, 2105])).
% 0.60/0.83 tff(2115,plain,
% 0.60/0.83 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[527, 2114, 1518])).
% 0.60/0.83 tff(2116,plain,
% 0.60/0.83 (~r(s(s(elem!1)), s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1222, 2111, 416])).
% 0.60/0.83 tff(2117,plain,
% 0.60/0.83 (b(s(s(elem!1)), s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[660, 2116, 244])).
% 0.60/0.83 tff(2118,plain,
% 0.60/0.83 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1616, 272, 2117, 2115])).
% 0.60/0.83 tff(2119,plain,
% 0.60/0.83 (r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[611, 139, 1477, 2118])).
% 0.60/0.83 tff(2120,plain,
% 0.60/0.83 (~r(s(s(elem!1)), elem!1)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[704, 2113, 637, 1477, 1434, 2105])).
% 0.60/0.83 tff(2121,plain,
% 0.60/0.83 (b(s(s(elem!1)), elem!1)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[843, 2120, 1481])).
% 0.60/0.83 tff(2122,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2123,plain,
% 0.60/0.83 (((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))) <=> ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2124,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2123])).
% 0.60/0.83 tff(2125,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[2124, 2122])).
% 0.60/0.83 tff(2126,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1)))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2127,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(elem!1)), elem!1)) | (~b(z, s(s(elem!1))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2126, 2125])).
% 0.60/0.83 tff(2128,plain,
% 0.60/0.83 (~b(z, s(s(elem!1)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2127, 272, 262, 2121])).
% 0.60/0.83 tff(2129,plain,
% 0.60/0.83 (r(z, s(s(elem!1)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[579, 2128])).
% 0.60/0.83 tff(2130,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2131,plain,
% 0.60/0.83 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2132,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2131])).
% 0.60/0.83 tff(2133,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[2132, 2130])).
% 0.60/0.83 tff(2134,plain,
% 0.60/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2135,plain,
% 0.60/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(s(elem!1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2134, 2133])).
% 0.60/0.83 tff(2136,plain,
% 0.60/0.83 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2135, 371, 2129, 2119])).
% 0.60/0.83 tff(2137,plain,
% 0.60/0.83 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1723, 2136])).
% 0.60/0.83 tff(2138,plain,
% 0.60/0.83 (r(z, s(elem!1)) <=> r(z, s(s(z)))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[249])).
% 0.60/0.83 tff(2139,plain,
% 0.60/0.83 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 0.60/0.83 inference(symmetry,[status(thm)],[2138])).
% 0.60/0.83 tff(2140,plain,
% 0.60/0.83 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[249])).
% 0.60/0.83 tff(2141,plain,
% 0.60/0.83 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2140])).
% 0.60/0.83 tff(2142,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2143,plain,
% 0.60/0.83 (((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1)))) <=> ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2144,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2143])).
% 0.60/0.83 tff(2145,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[2144, 2142])).
% 0.60/0.83 tff(2146,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(elem!1))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2147,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2146, 2145])).
% 0.60/0.83 tff(2148,plain,
% 0.60/0.83 (~b(z, s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2147, 272, 2113, 2107, 2137])).
% 0.60/0.83 tff(2149,plain,
% 0.60/0.83 (~b(z, s(s(z)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2148, 2141])).
% 0.60/0.83 tff(2150,plain,
% 0.60/0.83 (r(z, s(s(z)))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1073, 2149])).
% 0.60/0.83 tff(2151,plain,
% 0.60/0.83 (r(z, s(elem!1))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2150, 2139])).
% 0.60/0.83 tff(2152,assumption,(b(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.83 tff(2153,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2154,plain,
% 0.60/0.83 (((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2155,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2154])).
% 0.60/0.83 tff(2156,plain,
% 0.60/0.83 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[2155, 2153])).
% 0.60/0.83 tff(2157,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2158,plain,
% 0.60/0.83 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2157, 2156])).
% 0.60/0.83 tff(2159,plain,
% 0.60/0.83 (~b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2158, 272, 262, 2152, 767])).
% 0.60/0.83 tff(2160,plain,
% 0.60/0.83 (r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1734, 139, 170, 2159])).
% 0.60/0.83 tff(2161,plain,
% 0.60/0.83 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1699, 139, 1696, 1676])).
% 0.60/0.83 tff(2162,assumption,(r(z, s(elem!1))), introduced(assumption)).
% 0.60/0.83 tff(2163,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2164,plain,
% 0.60/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2165,plain,
% 0.60/0.83 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), z))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2164, 2163])).
% 0.60/0.83 tff(2166,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2165, 371, 2162, 2161, 2160])).
% 0.60/0.83 tff(2167,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(z, s(elem!1))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(2168,plain,
% 0.60/0.83 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2167, 2151, 1849, 262, 2137, 2113, 2107])).
% 0.60/0.83 tff(2169,plain,
% 0.60/0.83 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1784, 272, 2117, 2115])).
% 0.60/0.83 tff(2170,plain,
% 0.60/0.83 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[963, 139, 1476, 2169])).
% 0.60/0.83 tff(2171,assumption,(~b(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.83 tff(2172,plain,
% 0.60/0.83 ((s(s(s(s(s(s(elem!1)))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(symmetry,[status(thm)],[127])).
% 0.60/0.83 tff(2173,plain,
% 0.60/0.83 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(transitivity,[status(thm)],[1463, 2172])).
% 0.60/0.83 tff(2174,plain,
% 0.60/0.83 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2173])).
% 0.60/0.83 tff(2175,plain,
% 0.60/0.83 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[155, 2174])).
% 0.60/0.83 tff(2176,plain,
% 0.60/0.83 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2177,plain,
% 0.60/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(2178,plain,
% 0.60/0.83 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2177, 2176])).
% 0.60/0.83 tff(2179,plain,
% 0.60/0.83 ((elem!1 = s(s(s(s(s(s(elem!1))))))) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2178, 139])).
% 0.60/0.83 tff(2180,plain,
% 0.60/0.83 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2179, 2175, 2171])).
% 0.60/0.83 tff(2181,plain,
% 0.60/0.83 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.83 inference(commutativity,[status(thm)],[])).
% 0.60/0.83 tff(2182,plain,
% 0.60/0.83 ((~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2181])).
% 0.60/0.83 tff(2183,assumption,(elem!1 = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.83 tff(2184,plain,
% 0.60/0.83 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 0.60/0.83 inference(symmetry,[status(thm)],[2183])).
% 0.60/0.83 tff(2185,plain,
% 0.60/0.83 (s(s(s(s(s(s(s(elem!1))))))) = s(z)),
% 0.60/0.83 inference(transitivity,[status(thm)],[2184, 1427])).
% 0.60/0.83 tff(2186,plain,
% 0.60/0.83 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(z))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2185])).
% 0.60/0.83 tff(2187,plain,
% 0.60/0.83 (s(s(s(s(s(s(elem!1)))))) = z),
% 0.60/0.83 inference(transitivity,[status(thm)],[1640, 2186, 24])).
% 0.60/0.83 tff(2188,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[558, 2187])).
% 0.60/0.83 tff(2189,plain,((~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(2190,plain,
% 0.60/0.83 (~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2189, 53])).
% 0.60/0.83 tff(2191,plain,
% 0.60/0.83 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[2190, 2182])).
% 0.60/0.83 tff(2192,assumption,(~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.83 tff(2193,assumption,(~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 0.60/0.83 tff(2194,plain,
% 0.60/0.83 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[1445])).
% 0.60/0.83 tff(2195,plain,
% 0.60/0.83 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) <=> r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(symmetry,[status(thm)],[2194])).
% 0.60/0.83 tff(2196,plain,
% 0.60/0.83 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[944, 2195])).
% 0.60/0.83 tff(2197,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2193, 2196])).
% 0.60/0.83 tff(2198,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))) | r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(2199,plain,
% 0.60/0.83 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[2198, 2193, 944])).
% 0.60/0.83 tff(2200,plain,
% 0.60/0.83 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[1706, 2199, 2192])).
% 0.60/0.83 tff(2201,assumption,(r(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.83 tff(2202,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2203,plain,
% 0.60/0.83 (((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(2204,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[2203])).
% 0.60/0.83 tff(2205,plain,
% 0.60/0.83 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[2204, 2202])).
% 0.60/0.84 tff(2206,plain,
% 0.60/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(2207,plain,
% 0.60/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2206, 2205])).
% 0.60/0.84 tff(2208,plain,
% 0.60/0.84 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2207, 371, 2201, 2200])).
% 0.60/0.84 tff(2209,plain,
% 0.60/0.84 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1690, 2208, 1652])).
% 0.60/0.84 tff(2210,plain,
% 0.60/0.84 (b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1766, 2193, 1457])).
% 0.60/0.84 tff(2211,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1989, 272, 864, 2210, 2209])).
% 0.60/0.84 tff(2212,plain,(r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2213,plain,
% 0.60/0.84 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2212, 2121, 2191, 2180, 2168, 1444, 2170])).
% 0.60/0.84 tff(2214,plain,
% 0.60/0.84 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1761, 2213, 2170])).
% 0.60/0.84 tff(2215,plain,
% 0.60/0.84 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1706, 2214, 2168])).
% 0.60/0.84 tff(2216,plain,
% 0.60/0.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(symmetry,[status(thm)],[2215])).
% 0.60/0.84 tff(2217,plain,
% 0.60/0.84 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2216])).
% 0.60/0.84 tff(2218,plain,
% 0.60/0.84 (s(s(s(s(s(elem!1))))) = s(s(s(s(s(s(elem!1))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[33, 2217, 1436])).
% 0.60/0.84 tff(2219,plain,
% 0.60/0.84 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2218])).
% 0.60/0.84 tff(2220,plain,
% 0.60/0.84 (s(s(s(s(elem!1)))) = s(s(s(s(s(s(elem!1))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[38, 2219, 2217, 1436])).
% 0.60/0.84 tff(2221,plain,
% 0.60/0.84 (inj_0(s(s(s(s(elem!1))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2220])).
% 0.60/0.84 tff(2222,plain,
% 0.60/0.84 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(elem!1)))))),
% 0.60/0.84 inference(symmetry,[status(thm)],[2221])).
% 0.60/0.84 tff(2223,plain,
% 0.60/0.84 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(symmetry,[status(thm)],[2217])).
% 0.60/0.84 tff(2224,plain,
% 0.60/0.84 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[1640, 2223, 2222, 164])).
% 0.60/0.84 tff(2225,plain,
% 0.60/0.84 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2215])).
% 0.60/0.84 tff(2226,plain,
% 0.60/0.84 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2225])).
% 0.60/0.84 tff(2227,assumption,(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.60/0.84 tff(2228,plain,
% 0.60/0.84 (inj_0(s(s(s(s(s(s(s(elem!1)))))))) = inj_0(s(s(s(elem!1))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2227])).
% 0.60/0.84 tff(2229,plain,
% 0.60/0.84 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(symmetry,[status(thm)],[2228])).
% 0.60/0.84 tff(2230,plain,
% 0.60/0.84 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[602, 2229, 1436])).
% 0.60/0.84 tff(2231,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[177, 2230])).
% 0.60/0.84 tff(2232,plain,((~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2233,plain,
% 0.60/0.84 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2232, 1476])).
% 0.60/0.84 tff(2234,plain,
% 0.60/0.84 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2233, 2226])).
% 0.60/0.84 tff(2235,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2234, 2224])).
% 0.60/0.84 tff(2236,plain,((~(s(z) = elem!1)) | (~b(z, elem!1)) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | b(elem!1, s(s(s(s(s(s(elem!1))))))) | b(s(s(s(s(s(s(elem!1)))))), elem!1) | (~b(elem!1, z)) | (~b(s(z), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2237,plain,
% 0.60/0.84 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2236, 2103, 637, 416, 244, 2102, 2089, 1032, 2059])).
% 0.60/0.84 tff(2238,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2239,plain,
% 0.60/0.84 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2240,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2239])).
% 0.60/0.84 tff(2241,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[2240, 2238])).
% 0.60/0.84 tff(2242,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(2243,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2242, 2241])).
% 0.60/0.84 tff(2244,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2243, 272, 1032, 2237, 2100])).
% 0.60/0.84 tff(2245,plain,((~r(s(elem!1), elem!1)) | (~b(elem!1, z)) | (~r(s(elem!1), z)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(z), s(s(elem!1)))) | b(s(z), elem!1) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2246,plain,
% 0.60/0.84 (~r(s(elem!1), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2245, 2034, 1426, 2057, 2055, 129, 261])).
% 0.60/0.84 tff(2247,plain,
% 0.60/0.84 (b(s(elem!1), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[414, 2246])).
% 0.60/0.84 tff(2248,plain,
% 0.60/0.84 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1433, 144])).
% 0.60/0.84 tff(2249,plain,
% 0.60/0.84 (~r(z, elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[937, 2048, 1426, 2248, 2247])).
% 0.60/0.84 tff(2250,plain,
% 0.60/0.84 (b(z, elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[432, 2249, 261])).
% 0.60/0.84 tff(2251,plain,
% 0.60/0.84 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1443, 2248])).
% 0.60/0.84 tff(2252,plain,
% 0.60/0.84 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1460, 2251])).
% 0.60/0.84 tff(2253,plain,
% 0.60/0.84 (~(s(elem!1) = elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[246, 2057])).
% 0.60/0.84 tff(2254,plain,
% 0.60/0.84 (~(elem!1 = s(elem!1))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1558, 2253])).
% 0.60/0.84 tff(2255,plain,
% 0.60/0.84 (~b(elem!1, s(elem!1))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1569, 272, 2034, 2247])).
% 0.60/0.84 tff(2256,plain,
% 0.60/0.84 (r(elem!1, s(elem!1))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1574, 2255, 2254])).
% 0.60/0.84 tff(2257,plain,
% 0.60/0.84 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[181])).
% 0.60/0.84 tff(2258,plain,
% 0.60/0.84 (s(elem!1) = s(s(z))),
% 0.60/0.84 inference(symmetry,[status(thm)],[181])).
% 0.60/0.84 tff(2259,plain,
% 0.60/0.84 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2258])).
% 0.60/0.84 tff(2260,plain,
% 0.60/0.84 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2259])).
% 0.60/0.84 tff(2261,plain,
% 0.60/0.84 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1657, 156])).
% 0.60/0.84 tff(2262,plain,
% 0.60/0.84 (~b(s(s(elem!1)), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1040, 2034, 1858])).
% 0.60/0.84 tff(2263,plain,
% 0.60/0.84 (r(s(s(elem!1)), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[453, 2262])).
% 0.60/0.84 tff(2264,assumption,(b(z, s(elem!1))), introduced(assumption)).
% 0.60/0.84 tff(2265,plain,
% 0.60/0.84 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[527, 1156, 1736])).
% 0.60/0.84 tff(2266,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2267,plain,
% 0.60/0.84 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2268,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2267])).
% 0.60/0.84 tff(2269,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[2268, 2266])).
% 0.60/0.84 tff(2270,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(2271,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2270, 2269])).
% 0.60/0.84 tff(2272,plain,
% 0.60/0.84 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2271, 272, 2265, 2264])).
% 0.60/0.84 tff(2273,plain,
% 0.60/0.84 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1723, 2272])).
% 0.60/0.84 tff(2274,plain,
% 0.60/0.84 (~r(z, elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[937, 552, 637, 500, 399])).
% 0.60/0.84 tff(2275,plain,
% 0.60/0.84 (b(z, elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[432, 2274, 1362])).
% 0.60/0.84 tff(2276,plain,
% 0.60/0.84 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2277,plain,
% 0.60/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(2278,plain,
% 0.60/0.84 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2277, 2276])).
% 0.60/0.84 tff(2279,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2278, 371, 552, 752, 1752])).
% 0.60/0.84 tff(2280,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2281,plain,
% 0.60/0.84 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2280, 1752, 552])).
% 0.60/0.84 tff(2282,plain,
% 0.60/0.84 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1690, 2281, 1652])).
% 0.60/0.84 tff(2283,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2284,plain,
% 0.60/0.84 (((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2285,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2284])).
% 0.60/0.84 tff(2286,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[2285, 2283])).
% 0.60/0.84 tff(2287,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(2288,plain,
% 0.60/0.84 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), z))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[2287, 2286])).
% 0.60/0.84 tff(2289,plain,
% 0.60/0.84 (~b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2288, 272, 262, 2282])).
% 0.60/0.84 tff(2290,assumption,(r(z, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.84 tff(2291,plain,
% 0.60/0.84 (~r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1730, 371, 2290, 1752])).
% 0.60/0.84 tff(2292,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1734, 139, 170, 2291, 2289])).
% 0.60/0.84 tff(2293,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(2294,plain,
% 0.60/0.84 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[2293, 2275, 2273, 1652, 552])).
% 0.60/0.84 tff(2295,plain,
% 0.60/0.84 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[1706, 2294, 1648])).
% 0.60/0.84 tff(2296,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2297,plain,
% 0.60/0.84 (((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(2298,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[2297])).
% 0.60/0.84 tff(2299,plain,
% 0.60/0.84 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.84 inference(transitivity,[status(thm)],[2298, 2296])).
% 0.60/0.84 tff(2300,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(2301,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2300, 2299])).
% 0.60/0.85 tff(2302,plain,
% 0.60/0.85 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2301, 272, 399, 696, 2295])).
% 0.60/0.85 tff(2303,plain,
% 0.60/0.85 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1699, 139, 1696, 2302])).
% 0.60/0.85 tff(2304,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2305,plain,
% 0.60/0.85 (((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z))) <=> ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2306,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2305])).
% 0.60/0.85 tff(2307,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[2306, 2304])).
% 0.60/0.85 tff(2308,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(2309,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2308, 2307])).
% 0.60/0.85 tff(2310,plain,
% 0.60/0.85 (~b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2309, 272, 2275, 2265, 2264])).
% 0.60/0.85 tff(2311,plain,
% 0.60/0.85 (r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[562, 2310])).
% 0.60/0.85 tff(2312,plain,
% 0.60/0.85 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1774, 371, 1019, 2311])).
% 0.60/0.85 tff(2313,plain,
% 0.60/0.85 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[963, 139, 177, 2312])).
% 0.60/0.85 tff(2314,plain,
% 0.60/0.85 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1811, 272, 2295, 2313])).
% 0.60/0.85 tff(2315,plain,
% 0.60/0.85 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1766, 2314, 1647])).
% 0.60/0.85 tff(2316,plain,
% 0.60/0.85 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1181, 371, 1019, 2311])).
% 0.60/0.85 tff(2317,plain,
% 0.60/0.85 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[611, 139, 1649, 2316])).
% 0.60/0.85 tff(2318,plain,
% 0.60/0.85 (~b(s(s(elem!1)), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1618, 2317, 2265])).
% 0.60/0.85 tff(2319,plain,
% 0.60/0.85 (r(s(s(elem!1)), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[660, 2318, 244])).
% 0.60/0.85 tff(2320,plain,
% 0.60/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2321,plain,
% 0.60/0.85 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2322,plain,
% 0.60/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2321])).
% 0.60/0.85 tff(2323,plain,
% 0.60/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.85 inference(transitivity,[status(thm)],[2322, 2320])).
% 0.60/0.85 tff(2324,plain,
% 0.60/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(2325,plain,
% 0.60/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2324, 2323])).
% 0.60/0.85 tff(2326,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2325, 371, 2319, 2315, 2303])).
% 0.60/0.85 tff(2327,plain,((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | (~b(s(elem!1), z)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (s(s(elem!1)) = s(elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), z)) | (~b(z, s(elem!1))) | (s(elem!1) = s(s(s(s(s(s(elem!1))))))) | (~r(s(elem!1), elem!1)) | (z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(2328,plain,
% 0.60/0.85 (~b(z, s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2327, 2048, 2247, 2051, 2057, 173, 2263, 2261, 2248, 1426, 261])).
% 0.60/0.85 tff(2329,plain,
% 0.60/0.85 (~b(z, s(s(z)))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2328, 2260])).
% 0.60/0.85 tff(2330,plain,
% 0.60/0.85 (r(z, s(s(z)))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1073, 2329])).
% 0.60/0.85 tff(2331,plain,
% 0.60/0.85 (r(z, s(elem!1))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2330, 2257])).
% 0.60/0.85 tff(2332,plain,
% 0.60/0.85 (~r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2165, 371, 2162, 1841])).
% 0.60/0.85 tff(2333,plain,
% 0.60/0.85 (b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1734, 139, 170, 2332])).
% 0.60/0.85 tff(2334,assumption,(r(elem!1, s(elem!1))), introduced(assumption)).
% 0.60/0.85 tff(2335,plain,
% 0.60/0.85 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2336,plain,
% 0.60/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(2337,plain,
% 0.60/0.85 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2336, 2335])).
% 0.60/0.85 tff(2338,plain,
% 0.60/0.85 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2337, 371, 2334, 1841])).
% 0.60/0.85 tff(2339,plain,
% 0.60/0.85 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1690, 2338, 1652])).
% 0.60/0.85 tff(2340,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2288, 272, 262, 2339, 2333])).
% 0.60/0.85 tff(2341,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(z, elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~r(z, s(elem!1))) | (~r(elem!1, s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(2342,plain,
% 0.60/0.85 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2341, 2250, 2051, 2331, 2256])).
% 0.60/0.85 tff(2343,plain,
% 0.60/0.85 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1699, 139, 2261, 2342])).
% 0.60/0.85 tff(2344,plain,
% 0.60/0.85 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[502, 2248])).
% 0.60/0.85 tff(2345,plain,
% 0.60/0.85 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1155, 371, 1426, 2048])).
% 0.60/0.85 tff(2346,plain,
% 0.60/0.85 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[527, 2345, 2344])).
% 0.60/0.85 tff(2347,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2348,plain,
% 0.60/0.85 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2349,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2348])).
% 0.60/0.85 tff(2350,plain,
% 0.60/0.85 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(transitivity,[status(thm)],[2349, 2347])).
% 0.60/0.85 tff(2351,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(2352,plain,
% 0.60/0.85 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[2351, 2350])).
% 0.60/0.85 tff(2353,plain,
% 0.60/0.85 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2352, 272, 2346, 2343])).
% 0.60/0.85 tff(2354,plain,
% 0.60/0.85 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1706, 2353, 2252])).
% 0.60/0.85 tff(2355,plain,
% 0.60/0.85 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2293, 2354, 2250, 2051, 2048])).
% 0.60/0.85 tff(2356,plain,
% 0.60/0.85 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1723, 2355])).
% 0.60/0.85 tff(2357,plain,
% 0.60/0.85 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[690, 371, 1426, 2048])).
% 0.60/0.85 tff(2358,plain,
% 0.60/0.85 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[695, 2357, 2248])).
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% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(2360,plain,
% 0.60/0.85 (((~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), z)) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
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% 0.60/0.85 inference(monotonicity,[status(thm)],[2360])).
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% 0.60/0.85 inference(transitivity,[status(thm)],[2361, 2359])).
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% 0.60/0.85 inference(modus_ponens,[status(thm)],[2363, 2362])).
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[2364, 272, 2247, 2358, 2356])).
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% 0.60/0.85 tff(2367,plain,
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[2366, 126, 113, 100, 58])).
% 0.60/0.85 tff(2368,plain,((~(s(z) = elem!1)) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(2369,plain,
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[2368, 52])).
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[1418, 2369])).
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[235, 233])).
% 0.60/0.85 tff(2372,plain,
% 0.60/0.85 (~(s(s(elem!1)) = s(elem!1))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[98, 2371])).
% 0.60/0.85 tff(2373,plain,
% 0.60/0.85 (~(s(elem!1) = elem!1)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[246, 2372])).
% 0.60/0.85 tff(2374,assumption,(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.60/0.85 tff(2375,plain,
% 0.60/0.85 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(elem!1))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2374])).
% 0.60/0.85 tff(2376,plain,
% 0.60/0.85 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(symmetry,[status(thm)],[2375])).
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% 0.60/0.85 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 0.60/0.85 inference(transitivity,[status(thm)],[602, 2376, 32])).
% 0.60/0.85 tff(2378,plain,
% 0.60/0.85 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(elem!1))))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2377])).
% 0.60/0.85 tff(2379,plain,
% 0.60/0.85 (inj_0(s(s(s(s(s(elem!1)))))) = inj_0(s(s(elem!1)))),
% 0.60/0.85 inference(symmetry,[status(thm)],[2378])).
% 0.60/0.85 tff(2380,plain,
% 0.60/0.85 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(elem!1))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2374])).
% 0.60/0.85 tff(2381,plain,
% 0.60/0.85 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.60/0.85 inference(transitivity,[status(thm)],[2380, 38, 2379, 27])).
% 0.60/0.85 tff(2382,plain,
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[1696, 2381])).
% 0.60/0.85 tff(2383,plain,((~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(2384,plain,
% 0.60/0.85 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2383, 1658])).
% 0.60/0.85 tff(2385,plain,
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[1410, 221, 248])).
% 0.60/0.85 tff(2386,assumption,(s(s(z)) = s(s(elem!1))), introduced(assumption)).
% 0.60/0.85 tff(2387,plain,
% 0.60/0.85 (inj_0(s(s(z))) = inj_0(s(s(elem!1)))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2386])).
% 0.60/0.85 tff(2388,plain,
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% 0.60/0.85 inference(symmetry,[status(thm)],[2387])).
% 0.60/0.85 tff(2389,plain,
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% 0.60/0.85 inference(transitivity,[status(thm)],[68, 2388, 212])).
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% 0.60/0.85 inference(unit_resolution,[status(thm)],[11, 2389])).
% 0.60/0.85 tff(2391,plain,((~(s(s(z)) = s(s(elem!1)))) | (s(elem!1) = s(z))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(2392,plain,
% 0.60/0.85 (s(elem!1) = s(z)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[2391, 2385])).
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% 0.60/0.85 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[50, 2392])).
% 0.60/0.85 tff(2394,plain,
% 0.60/0.85 (z = elem!1),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[1886, 2392])).
% 0.60/0.85 tff(2395,plain,
% 0.60/0.85 ((s(elem!1) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.60/0.85 inference(symmetry,[status(thm)],[497])).
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% 0.60/0.85 tff(2397,plain,
% 0.60/0.85 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[2396])).
% 0.60/0.86 tff(2398,plain,
% 0.60/0.86 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2397, 2395])).
% 0.60/0.86 tff(2399,plain,
% 0.60/0.86 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1)))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2398])).
% 0.60/0.86 tff(2400,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[155, 2399])).
% 0.60/0.86 tff(2401,assumption,(~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.86 tff(2402,plain,
% 0.60/0.86 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(elem!1) = s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2397])).
% 0.60/0.86 tff(2403,plain,
% 0.60/0.86 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[155, 2402])).
% 0.60/0.86 tff(2404,plain,
% 0.60/0.86 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1443, 2403])).
% 0.60/0.86 tff(2405,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1460, 2404])).
% 0.60/0.86 tff(2406,plain,
% 0.60/0.86 ((s(s(s(elem!1))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 0.60/0.86 inference(commutativity,[status(thm)],[])).
% 0.60/0.86 tff(2407,plain,
% 0.60/0.86 ((s(s(s(elem!1))) = z) <=> (s(s(s(elem!1))) = elem!1)),
% 0.60/0.86 inference(monotonicity,[status(thm)],[1])).
% 0.60/0.86 tff(2408,plain,
% 0.60/0.86 ((s(s(s(elem!1))) = z) <=> (elem!1 = s(s(s(elem!1))))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2407, 2406])).
% 0.60/0.86 tff(2409,plain,
% 0.60/0.86 ((~(s(s(s(elem!1))) = z)) <=> (~(elem!1 = s(s(s(elem!1)))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2408])).
% 0.60/0.86 tff(2410,plain,
% 0.60/0.86 (~(elem!1 = s(s(s(elem!1))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[73, 2409])).
% 0.60/0.86 tff(2411,assumption,(s(s(elem!1)) = s(s(s(elem!1)))), introduced(assumption)).
% 0.60/0.86 tff(2412,plain,
% 0.60/0.86 (inj_0(s(s(elem!1))) = inj_0(s(s(s(elem!1))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2411])).
% 0.60/0.86 tff(2413,plain,
% 0.60/0.86 (s(z) = s(s(s(elem!1)))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2396, 68, 2412, 601, 2411])).
% 0.60/0.86 tff(2414,plain,
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% 0.60/0.86 inference(unit_resolution,[status(thm)],[605, 2413])).
% 0.60/0.86 tff(2415,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.86 tff(2416,plain,
% 0.60/0.86 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2415, 1])).
% 0.60/0.86 tff(2417,plain,
% 0.60/0.86 (s(elem!1) = s(z)),
% 0.60/0.86 inference(symmetry,[status(thm)],[2396])).
% 0.60/0.86 tff(2418,plain,
% 0.60/0.86 (b(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.86 tff(2419,plain,
% 0.60/0.86 (b(s(z), s(s(s(s(s(s(s(elem!1)))))))) <=> b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(symmetry,[status(thm)],[2418])).
% 0.60/0.86 tff(2420,assumption,(s(z) = s(s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.86 tff(2421,plain,
% 0.60/0.86 (s(s(s(s(s(s(s(elem!1))))))) = s(z)),
% 0.60/0.86 inference(symmetry,[status(thm)],[2420])).
% 0.60/0.86 tff(2422,plain,
% 0.60/0.86 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.60/0.86 inference(transitivity,[status(thm)],[2421, 2396])).
% 0.60/0.86 tff(2423,plain,
% 0.60/0.86 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.60/0.86 inference(monotonicity,[status(thm)],[1])).
% 0.60/0.86 tff(2424,plain,
% 0.60/0.86 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2423])).
% 0.60/0.86 tff(2425,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[558, 2424])).
% 0.60/0.86 tff(2426,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1657, 2425])).
% 0.60/0.86 tff(2427,plain,
% 0.60/0.86 ($false),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2426, 2422])).
% 0.60/0.86 tff(2428,plain,((~(s(z) = s(s(s(s(s(s(s(elem!1))))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.86 tff(2429,plain,
% 0.60/0.86 (~(s(z) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2428, 1])).
% 0.60/0.86 tff(2430,plain,
% 0.60/0.86 (r(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.86 tff(2431,plain,
% 0.60/0.86 ((~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) <=> (~r(s(z), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2430])).
% 0.60/0.86 tff(2432,plain,
% 0.60/0.86 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.86 inference(monotonicity,[status(thm)],[1])).
% 0.60/0.86 tff(2433,plain,
% 0.60/0.86 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2432])).
% 0.60/0.86 tff(2434,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[170, 2433])).
% 0.60/0.86 tff(2435,plain,
% 0.60/0.86 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.86 tff(2436,plain,
% 0.60/0.86 (b(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.86 inference(symmetry,[status(thm)],[2435])).
% 0.60/0.86 tff(2437,plain,
% 0.60/0.86 ((s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.86 tff(2438,plain,
% 0.60/0.86 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = s(z)))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2437])).
% 0.60/0.86 tff(2439,plain,
% 0.60/0.86 (~(s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2426, 2438])).
% 0.60/0.86 tff(2440,plain,
% 0.60/0.86 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1847, 1842, 1752])).
% 0.60/0.86 tff(2441,plain,
% 0.60/0.86 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.86 tff(2442,plain,
% 0.60/0.86 (r(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.86 inference(symmetry,[status(thm)],[2441])).
% 0.60/0.86 tff(2443,plain,
% 0.60/0.86 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[1999, 2442])).
% 0.60/0.86 tff(2444,assumption,(~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))), introduced(assumption)).
% 0.60/0.86 tff(2445,plain,
% 0.60/0.86 ($false),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2444, 2443])).
% 0.60/0.86 tff(2446,plain,(r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.86 tff(2447,plain,
% 0.60/0.86 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2446, 2440, 1])).
% 0.60/0.86 tff(2448,plain,
% 0.60/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) | b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z)))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(z)) | b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2449,plain,
% 0.60/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) | b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2450,plain,
% 0.60/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(z)) | b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2449, 2448])).
% 0.60/0.86 tff(2451,plain,
% 0.60/0.86 ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) | b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2450, 139])).
% 0.60/0.86 tff(2452,plain,
% 0.60/0.86 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2451, 2447, 2439])).
% 0.60/0.86 tff(2453,plain,
% 0.60/0.86 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2452, 2436])).
% 0.60/0.86 tff(2454,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2455,plain,
% 0.60/0.86 (((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2456,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2455])).
% 0.60/0.86 tff(2457,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2456, 2454])).
% 0.60/0.86 tff(2458,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2459,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2458, 2457])).
% 0.60/0.86 tff(2460,plain,
% 0.60/0.86 ($false),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2459, 272, 291, 1677, 2025])).
% 0.60/0.86 tff(2461,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.86 tff(2462,plain,
% 0.60/0.86 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2461, 2453, 291])).
% 0.60/0.86 tff(2463,plain,
% 0.60/0.86 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1690, 2462, 2434])).
% 0.60/0.86 tff(2464,plain,
% 0.60/0.86 (~r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2280, 2463, 1752])).
% 0.60/0.86 tff(2465,plain,
% 0.60/0.86 (b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[545, 2464, 2425])).
% 0.60/0.86 tff(2466,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2467,plain,
% 0.60/0.86 (((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2468,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2467])).
% 0.60/0.86 tff(2469,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2468, 2466])).
% 0.60/0.86 tff(2470,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2471,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2470, 2469])).
% 0.60/0.86 tff(2472,plain,
% 0.60/0.86 (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2471, 272, 291, 2465])).
% 0.60/0.86 tff(2473,plain,
% 0.60/0.86 (r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[695, 2472, 2403])).
% 0.60/0.86 tff(2474,plain,
% 0.60/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2475,plain,
% 0.60/0.86 (((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2476,plain,
% 0.60/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2475])).
% 0.60/0.86 tff(2477,plain,
% 0.60/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2476, 2474])).
% 0.60/0.86 tff(2478,plain,
% 0.60/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2479,plain,
% 0.60/0.86 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2478, 2477])).
% 0.60/0.86 tff(2480,plain,
% 0.60/0.86 (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2479, 371, 2473, 1752])).
% 0.60/0.86 tff(2481,plain,
% 0.60/0.86 (~r(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2480, 2431])).
% 0.60/0.86 tff(2482,plain,
% 0.60/0.86 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(z), s(s(s(s(s(s(s(elem!1)))))))) | r(s(z), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(z), s(s(s(s(s(s(s(elem!1)))))))) | r(s(z), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2483,plain,
% 0.60/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(z), s(s(s(s(s(s(s(elem!1)))))))) | r(s(z), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2484,plain,
% 0.60/0.86 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(z), s(s(s(s(s(s(s(elem!1)))))))) | r(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2483, 2482])).
% 0.60/0.86 tff(2485,plain,
% 0.60/0.86 ((s(z) = s(s(s(s(s(s(s(elem!1)))))))) | b(s(z), s(s(s(s(s(s(s(elem!1)))))))) | r(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2484, 139])).
% 0.60/0.86 tff(2486,plain,
% 0.60/0.86 (b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2485, 2481, 2429])).
% 0.60/0.86 tff(2487,plain,
% 0.60/0.86 (b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2486, 2419])).
% 0.60/0.86 tff(2488,plain,
% 0.60/0.86 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1818, 371, 254, 2463])).
% 0.60/0.86 tff(2489,plain,
% 0.60/0.86 (b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[1766, 2488, 2404])).
% 0.60/0.86 tff(2490,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2491,plain,
% 0.60/0.86 (((~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2492,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[2491])).
% 0.60/0.86 tff(2493,plain,
% 0.60/0.86 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.86 inference(transitivity,[status(thm)],[2492, 2490])).
% 0.60/0.86 tff(2494,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(2495,plain,
% 0.60/0.86 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[2494, 2493])).
% 0.60/0.86 tff(2496,plain,
% 0.60/0.86 ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2495, 272, 2489])).
% 0.60/0.86 tff(2497,plain,
% 0.60/0.86 (~b(s(s(elem!1)), s(elem!1))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[2496, 2487])).
% 0.60/0.86 tff(2498,plain,
% 0.60/0.86 (r(s(s(elem!1)), s(elem!1))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[660, 2497, 244])).
% 0.60/0.86 tff(2499,plain,
% 0.60/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2500,plain,
% 0.60/0.86 (((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(2501,plain,
% 0.60/0.86 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2500])).
% 0.60/0.87 tff(2502,plain,
% 0.60/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.60/0.87 inference(transitivity,[status(thm)],[2501, 2499])).
% 0.60/0.87 tff(2503,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2504,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 0.60/0.87 tff(2505,plain,
% 0.60/0.87 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2504, 371, 2498, 1842])).
% 0.60/0.87 tff(2506,plain,
% 0.60/0.87 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[963, 139, 177, 2505])).
% 0.60/0.87 tff(2507,plain,
% 0.60/0.87 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2383, 2426])).
% 0.60/0.87 tff(2508,plain,
% 0.60/0.87 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2232, 177])).
% 0.60/0.87 tff(2509,assumption,(b(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2510,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2511,assumption,(b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2512,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2513,plain,
% 0.60/0.87 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2514,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2513])).
% 0.60/0.87 tff(2515,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.87 inference(transitivity,[status(thm)],[2514, 2512])).
% 0.60/0.87 tff(2516,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2517,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2516, 2515])).
% 0.60/0.87 tff(2518,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2517, 272, 2511, 2509, 1805])).
% 0.60/0.87 tff(2519,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2520,plain,
% 0.60/0.87 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2519, 2509, 1805])).
% 0.60/0.87 tff(2521,plain,
% 0.60/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2522,plain,
% 0.60/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2523,plain,
% 0.60/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2522, 2521])).
% 0.60/0.87 tff(2524,plain,
% 0.60/0.87 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2523, 139])).
% 0.60/0.87 tff(2525,plain,
% 0.60/0.87 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2524, 2520, 2401])).
% 0.60/0.87 tff(2526,assumption,(r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2527,assumption,(r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2528,plain,
% 0.60/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2529,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2530,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2529, 2528])).
% 0.60/0.87 tff(2531,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2530, 371, 2527, 2526, 1752])).
% 0.60/0.87 tff(2532,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2533,plain,
% 0.60/0.87 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2532, 2525, 1752])).
% 0.60/0.87 tff(2534,plain,
% 0.60/0.87 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2535,plain,
% 0.60/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2536,plain,
% 0.60/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2535, 2534])).
% 0.60/0.87 tff(2537,plain,
% 0.60/0.87 ((s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1)))) | r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2536, 139])).
% 0.60/0.87 tff(2538,plain,
% 0.60/0.87 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2537, 2533, 2510])).
% 0.60/0.87 tff(2539,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2540,plain,
% 0.60/0.87 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2541,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2540])).
% 0.60/0.87 tff(2542,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.87 inference(transitivity,[status(thm)],[2541, 2539])).
% 0.60/0.87 tff(2543,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2544,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2543, 2542])).
% 0.60/0.87 tff(2545,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2544, 272, 2538, 1983, 2509])).
% 0.60/0.87 tff(2546,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2547,plain,
% 0.60/0.87 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2546, 2489, 2508, 1752, 2507, 2506])).
% 0.60/0.87 tff(2548,plain,
% 0.60/0.87 (((~![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)))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2549,plain,
% 0.60/0.87 ((~![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)))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2550,plain,
% 0.60/0.87 ((~![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))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2549, 2548])).
% 0.60/0.87 tff(2551,plain,
% 0.60/0.87 ((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))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2550, 139])).
% 0.60/0.87 tff(2552,plain,
% 0.60/0.87 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2551, 2547, 2416])).
% 0.60/0.87 tff(2553,assumption,(r(s(s(elem!1)), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2554,assumption,(r(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2555,plain,
% 0.60/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2556,plain,
% 0.60/0.87 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2557,plain,
% 0.60/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2556])).
% 0.60/0.87 tff(2558,plain,
% 0.60/0.87 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(transitivity,[status(thm)],[2557, 2555])).
% 0.60/0.87 tff(2559,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2560,plain,
% 0.60/0.87 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 0.60/0.87 tff(2561,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2560, 371, 254, 2554, 2553])).
% 0.60/0.87 tff(2562,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2563,plain,
% 0.60/0.87 (~r(elem!1, s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2562, 2552, 254])).
% 0.60/0.87 tff(2564,plain,
% 0.60/0.87 (((~![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)))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2565,plain,
% 0.60/0.87 ((~![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)))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2566,plain,
% 0.60/0.87 ((~![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))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2565, 2564])).
% 0.60/0.87 tff(2567,plain,
% 0.60/0.87 ((elem!1 = s(s(s(elem!1)))) | b(elem!1, s(s(s(elem!1)))) | r(elem!1, s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2566, 139])).
% 0.60/0.87 tff(2568,plain,
% 0.60/0.87 (b(elem!1, s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2567, 2563, 2410])).
% 0.60/0.87 tff(2569,assumption,(b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2570,assumption,(b(elem!1, s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2571,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2572,plain,
% 0.60/0.87 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1))) <=> ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2573,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2572])).
% 0.60/0.87 tff(2574,plain,
% 0.60/0.87 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.60/0.87 inference(transitivity,[status(thm)],[2573, 2571])).
% 0.60/0.87 tff(2575,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2576,plain,
% 0.60/0.87 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2575, 2574])).
% 0.60/0.87 tff(2577,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2576, 272, 291, 2570, 2569])).
% 0.60/0.87 tff(2578,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2579,plain,
% 0.60/0.87 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2578, 2568, 291])).
% 0.60/0.87 tff(2580,plain,
% 0.60/0.87 (b(s(elem!1), s(s(s(elem!1)))) <=> b(s(z), s(s(s(elem!1))))),
% 0.60/0.87 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.87 tff(2581,plain,
% 0.60/0.87 (b(s(z), s(s(s(elem!1)))) <=> b(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.87 inference(symmetry,[status(thm)],[2580])).
% 0.60/0.87 tff(2582,assumption,(b(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2583,plain,
% 0.60/0.87 (b(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.87 inference(modus_ponens,[status(thm)],[2582, 2581])).
% 0.60/0.87 tff(2584,assumption,(~b(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.87 tff(2585,plain,
% 0.60/0.87 ($false),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2584, 2583])).
% 0.60/0.87 tff(2586,plain,(b(s(elem!1), s(s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.87 tff(2587,plain,
% 0.60/0.87 (~b(s(z), s(s(s(elem!1))))),
% 0.60/0.87 inference(unit_resolution,[status(thm)],[2586, 2579, 1])).
% 0.60/0.87 tff(2588,plain,
% 0.60/0.87 (((~![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)))))),
% 0.60/0.87 inference(rewrite,[status(thm)],[])).
% 0.60/0.87 tff(2589,plain,
% 0.60/0.87 ((~![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)))))),
% 0.60/0.87 inference(quant_inst,[status(thm)],[])).
% 0.60/0.87 tff(2590,plain,
% 0.60/0.87 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2589, 2588])).
% 0.60/0.88 tff(2591,plain,
% 0.60/0.88 ((s(z) = s(s(s(elem!1)))) | b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2590, 139])).
% 0.60/0.88 tff(2592,plain,
% 0.60/0.88 (b(s(z), s(s(s(elem!1)))) | r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2591, 605])).
% 0.60/0.88 tff(2593,plain,
% 0.60/0.88 (r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2592, 2587])).
% 0.60/0.88 tff(2594,plain,
% 0.60/0.88 (r(s(elem!1), s(s(s(elem!1)))) <=> r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2417])).
% 0.60/0.88 tff(2595,plain,
% 0.60/0.88 (r(s(z), s(s(s(elem!1)))) <=> r(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.88 inference(symmetry,[status(thm)],[2594])).
% 0.60/0.88 tff(2596,assumption,(r(s(z), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.88 tff(2597,plain,
% 0.60/0.88 (r(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2596, 2595])).
% 0.60/0.88 tff(2598,assumption,(~r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.88 tff(2599,plain,
% 0.60/0.88 ($false),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2598, 2597])).
% 0.60/0.88 tff(2600,plain,(r(s(elem!1), s(s(s(elem!1)))) | (~r(s(z), s(s(s(elem!1))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.88 tff(2601,plain,
% 0.60/0.88 (r(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2600, 2593, 1])).
% 0.60/0.88 tff(2602,assumption,(r(s(elem!1), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.88 tff(2603,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2604,plain,
% 0.60/0.88 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2605,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2604])).
% 0.60/0.88 tff(2606,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.88 inference(transitivity,[status(thm)],[2605, 2603])).
% 0.60/0.88 tff(2607,plain,
% 0.60/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.60/0.88 inference(quant_inst,[status(thm)],[])).
% 0.60/0.88 tff(2608,plain,
% 0.60/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2607, 2606])).
% 0.60/0.88 tff(2609,plain,
% 0.60/0.88 ($false),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2608, 371, 1842, 2526, 2602])).
% 0.60/0.88 tff(2610,plain,((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.88 tff(2611,plain,
% 0.60/0.88 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2610, 2601, 1842])).
% 0.60/0.88 tff(2612,plain,
% 0.60/0.88 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2524, 2611, 2507])).
% 0.60/0.88 tff(2613,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2614,plain,
% 0.60/0.88 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2615,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2614])).
% 0.60/0.88 tff(2616,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(transitivity,[status(thm)],[2615, 2613])).
% 0.60/0.88 tff(2617,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.60/0.88 inference(quant_inst,[status(thm)],[])).
% 0.60/0.88 tff(2618,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2617, 2616])).
% 0.60/0.88 tff(2619,plain,
% 0.60/0.88 ($false),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2618, 272, 2465, 2612, 2568])).
% 0.60/0.88 tff(2620,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.88 tff(2621,plain,
% 0.60/0.88 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2620, 1842, 1, 291, 254, 177, 244])).
% 0.60/0.88 tff(2622,plain,
% 0.60/0.88 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[1706, 2621, 2405])).
% 0.60/0.88 tff(2623,assumption,(b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.88 tff(2624,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2625,plain,
% 0.60/0.88 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2626,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2625])).
% 0.60/0.88 tff(2627,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.88 inference(transitivity,[status(thm)],[2626, 2624])).
% 0.60/0.88 tff(2628,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.88 inference(quant_inst,[status(thm)],[])).
% 0.60/0.88 tff(2629,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2628, 2627])).
% 0.60/0.88 tff(2630,plain,
% 0.60/0.88 ($false),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2629, 272, 2623, 2511, 767])).
% 0.60/0.88 tff(2631,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.88 tff(2632,plain,
% 0.60/0.88 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2631, 2511, 767])).
% 0.60/0.88 tff(2633,plain,
% 0.60/0.88 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2537, 2632, 2508])).
% 0.60/0.88 tff(2634,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2635,plain,
% 0.60/0.88 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2636,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2635])).
% 0.60/0.88 tff(2637,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.88 inference(transitivity,[status(thm)],[2636, 2634])).
% 0.60/0.88 tff(2638,plain,
% 0.60/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.88 inference(quant_inst,[status(thm)],[])).
% 0.60/0.88 tff(2639,plain,
% 0.60/0.88 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2638, 2637])).
% 0.60/0.88 tff(2640,plain,
% 0.60/0.88 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2639, 371, 2527, 2554])).
% 0.60/0.88 tff(2641,plain,
% 0.60/0.88 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[1690, 2640, 1652])).
% 0.60/0.88 tff(2642,plain,
% 0.60/0.88 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[1685, 2641, 767])).
% 0.60/0.88 tff(2643,plain,
% 0.60/0.88 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[545, 2642, 221])).
% 0.60/0.88 tff(2644,plain,
% 0.60/0.88 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[549, 371, 254, 2643])).
% 0.60/0.88 tff(2645,assumption,(~(s(s(elem!1)) = s(s(s(elem!1))))), introduced(assumption)).
% 0.60/0.88 tff(2646,plain,
% 0.60/0.88 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2562, 2554, 254])).
% 0.60/0.88 tff(2647,plain,
% 0.60/0.88 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2551, 2646, 2645])).
% 0.60/0.88 tff(2648,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2649,plain,
% 0.60/0.88 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2650,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2649])).
% 0.60/0.88 tff(2651,plain,
% 0.60/0.88 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.88 inference(transitivity,[status(thm)],[2650, 2648])).
% 0.60/0.88 tff(2652,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.60/0.88 inference(quant_inst,[status(thm)],[])).
% 0.60/0.88 tff(2653,plain,
% 0.60/0.88 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.88 inference(modus_ponens,[status(thm)],[2652, 2651])).
% 0.60/0.88 tff(2654,plain,
% 0.60/0.88 (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2653, 272, 2511, 2647])).
% 0.60/0.88 tff(2655,plain,
% 0.60/0.88 ($false),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[611, 139, 662, 2654, 2644])).
% 0.60/0.88 tff(2656,plain,((~r(elem!1, s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.88 tff(2657,plain,
% 0.60/0.88 (~r(elem!1, s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2656, 2511, 254, 2425, 767, 2434, 1649, 2633, 2416])).
% 0.60/0.88 tff(2658,plain,
% 0.60/0.88 (b(elem!1, s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2567, 2657, 2410])).
% 0.60/0.88 tff(2659,plain,
% 0.60/0.88 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2578, 2658, 291])).
% 0.60/0.88 tff(2660,plain,
% 0.60/0.88 (~b(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2586, 2659, 1])).
% 0.60/0.88 tff(2661,plain,
% 0.60/0.88 (r(s(z), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2592, 2660])).
% 0.60/0.88 tff(2662,plain,
% 0.60/0.88 (r(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.88 inference(unit_resolution,[status(thm)],[2600, 2661, 1])).
% 0.60/0.88 tff(2663,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2664,plain,
% 0.60/0.88 (((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.88 inference(rewrite,[status(thm)],[])).
% 0.60/0.88 tff(2665,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 0.60/0.88 inference(monotonicity,[status(thm)],[2664])).
% 0.60/0.88 tff(2666,plain,
% 0.60/0.88 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2665, 2663])).
% 0.60/0.89 tff(2667,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.60/0.89 inference(quant_inst,[status(thm)],[])).
% 0.60/0.89 tff(2668,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2667, 2666])).
% 0.60/0.89 tff(2669,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2668, 371, 2633, 2662])).
% 0.60/0.89 tff(2670,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2446, 2669, 1])).
% 0.60/0.89 tff(2671,plain,
% 0.60/0.89 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2451, 2670, 2439])).
% 0.60/0.89 tff(2672,plain,
% 0.60/0.89 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2671, 2436])).
% 0.60/0.89 tff(2673,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2461, 2672, 291])).
% 0.60/0.89 tff(2674,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1690, 2673, 2434])).
% 0.60/0.89 tff(2675,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2618, 272, 2511, 2658])).
% 0.60/0.89 tff(2676,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[545, 2675, 2425])).
% 0.60/0.89 tff(2677,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2678,plain,
% 0.60/0.89 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2679,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2678])).
% 0.60/0.89 tff(2680,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2679, 2677])).
% 0.60/0.89 tff(2681,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(quant_inst,[status(thm)],[])).
% 0.60/0.89 tff(2682,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2681, 2680])).
% 0.60/0.89 tff(2683,plain,
% 0.60/0.89 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2682, 371, 254, 2676])).
% 0.60/0.89 tff(2684,plain,
% 0.60/0.89 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[963, 139, 177, 2683])).
% 0.60/0.89 tff(2685,plain,
% 0.60/0.89 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1811, 272, 767, 2684])).
% 0.60/0.89 tff(2686,plain,
% 0.60/0.89 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1766, 2685, 2404])).
% 0.60/0.89 tff(2687,plain,
% 0.60/0.89 ($false),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1818, 371, 254, 2686, 2674])).
% 0.60/0.89 tff(2688,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.89 tff(2689,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2688, 2622, 291, 1, 254, 177])).
% 0.60/0.89 tff(2690,plain,
% 0.60/0.89 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2610, 2526, 1842])).
% 0.60/0.89 tff(2691,plain,
% 0.60/0.89 (~r(s(z), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2600, 2690, 1])).
% 0.60/0.89 tff(2692,plain,
% 0.60/0.89 (b(s(z), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2592, 2691])).
% 0.60/0.89 tff(2693,plain,
% 0.60/0.89 (b(s(elem!1), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2586, 2692, 1])).
% 0.60/0.89 tff(2694,plain,
% 0.60/0.89 (~b(elem!1, s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2578, 2693, 291])).
% 0.60/0.89 tff(2695,plain,
% 0.60/0.89 (r(elem!1, s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2567, 2694, 2410])).
% 0.60/0.89 tff(2696,plain,
% 0.60/0.89 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2562, 2695, 254])).
% 0.60/0.89 tff(2697,plain,
% 0.60/0.89 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2551, 2696, 2416])).
% 0.60/0.89 tff(2698,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2699,plain,
% 0.60/0.89 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2700,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2699])).
% 0.60/0.89 tff(2701,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2700, 2698])).
% 0.60/0.89 tff(2702,plain,
% 0.60/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.60/0.89 inference(quant_inst,[status(thm)],[])).
% 0.60/0.89 tff(2703,plain,
% 0.60/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(s(elem!1)))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2702, 2701])).
% 0.60/0.89 tff(2704,plain,
% 0.60/0.89 (~b(s(s(elem!1)), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2703, 272, 291, 2697, 2693])).
% 0.60/0.89 tff(2705,plain,
% 0.60/0.89 (r(s(s(elem!1)), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[660, 2704, 244])).
% 0.60/0.89 tff(2706,plain,
% 0.60/0.89 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2504, 371, 2705, 1842])).
% 0.60/0.89 tff(2707,plain,
% 0.60/0.89 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[963, 139, 177, 2706])).
% 0.60/0.89 tff(2708,plain,
% 0.60/0.89 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2423, 2172])).
% 0.60/0.89 tff(2709,plain,
% 0.60/0.89 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2708])).
% 0.60/0.89 tff(2710,plain,
% 0.60/0.89 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[558, 2709])).
% 0.60/0.89 tff(2711,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2712,plain,
% 0.60/0.89 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2713,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2712])).
% 0.60/0.89 tff(2714,plain,
% 0.60/0.89 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2713, 2711])).
% 0.60/0.89 tff(2715,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(quant_inst,[status(thm)],[])).
% 0.60/0.89 tff(2716,plain,
% 0.60/0.89 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2715, 2714])).
% 0.60/0.89 tff(2717,plain,
% 0.60/0.89 ($false),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2716, 371, 2201, 2526, 2554])).
% 0.60/0.89 tff(2718,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.89 tff(2719,plain,
% 0.60/0.89 (~r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2718, 2695, 2526])).
% 0.60/0.89 tff(2720,plain,
% 0.60/0.89 (b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2179, 2719, 2710])).
% 0.60/0.89 tff(2721,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2722,plain,
% 0.60/0.89 (((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(rewrite,[status(thm)],[])).
% 0.60/0.89 tff(2723,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2722])).
% 0.60/0.89 tff(2724,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2723, 2721])).
% 0.60/0.89 tff(2725,plain,
% 0.60/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.60/0.89 inference(quant_inst,[status(thm)],[])).
% 0.60/0.89 tff(2726,plain,
% 0.60/0.89 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[2725, 2724])).
% 0.60/0.89 tff(2727,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2726, 272, 2720, 767])).
% 0.60/0.89 tff(2728,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1690, 2727, 2434])).
% 0.60/0.89 tff(2729,plain,
% 0.60/0.89 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1818, 371, 254, 2728])).
% 0.60/0.89 tff(2730,plain,
% 0.60/0.89 (b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1766, 2729, 2404])).
% 0.60/0.89 tff(2731,plain,
% 0.60/0.89 ($false),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[1811, 272, 2730, 767, 2707])).
% 0.60/0.89 tff(2732,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.89 tff(2733,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2732, 2622, 177, 1, 1842, 244, 291, 254])).
% 0.60/0.89 tff(2734,plain,
% 0.60/0.89 ($false),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2524, 2733, 2689, 2401])).
% 0.60/0.89 tff(2735,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.89 tff(2736,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2735, 254, 177, 1, 237, 291, 2384])).
% 0.60/0.89 tff(2737,plain,
% 0.60/0.89 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[527, 2736, 2400])).
% 0.60/0.89 tff(2738,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[522, 2737, 291])).
% 0.60/0.89 tff(2739,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[545, 2738, 221])).
% 0.60/0.89 tff(2740,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[549, 371, 254, 2739])).
% 0.60/0.89 tff(2741,plain,
% 0.60/0.89 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[611, 139, 1649, 2740])).
% 0.60/0.89 tff(2742,plain,
% 0.60/0.89 (r(s(s(elem!1)), z) <=> r(s(s(elem!1)), elem!1)),
% 0.60/0.89 inference(monotonicity,[status(thm)],[1])).
% 0.60/0.89 tff(2743,plain,
% 0.60/0.89 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), z)),
% 0.60/0.89 inference(symmetry,[status(thm)],[2742])).
% 0.60/0.89 tff(2744,plain,
% 0.60/0.89 (r(s(s(elem!1)), z)),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[254, 2743])).
% 0.60/0.89 tff(2745,plain,
% 0.60/0.89 (r(s(s(elem!1)), elem!1)),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[1019, 2742])).
% 0.60/0.89 tff(2746,plain,
% 0.60/0.89 ((~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), s(z)))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2435])).
% 0.60/0.89 tff(2747,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2688, 767, 291, 1, 254, 177])).
% 0.60/0.89 tff(2748,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2524, 2747, 2507])).
% 0.60/0.89 tff(2749,plain,
% 0.60/0.89 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2732, 2748, 177, 767, 254, 244, 291, 1])).
% 0.60/0.89 tff(2750,plain,
% 0.60/0.89 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[527, 2749, 2400])).
% 0.60/0.89 tff(2751,plain,
% 0.60/0.89 ((s(s(elem!1)) = z) <=> (s(s(elem!1)) = elem!1)),
% 0.60/0.89 inference(monotonicity,[status(thm)],[1])).
% 0.60/0.89 tff(2752,plain,
% 0.60/0.89 ((s(s(elem!1)) = z) <=> (elem!1 = s(s(elem!1)))),
% 0.60/0.89 inference(transitivity,[status(thm)],[2751, 78])).
% 0.60/0.89 tff(2753,plain,
% 0.60/0.89 ((~(s(s(elem!1)) = z)) <=> (~(elem!1 = s(s(elem!1))))),
% 0.60/0.89 inference(monotonicity,[status(thm)],[2752])).
% 0.60/0.89 tff(2754,plain,
% 0.60/0.89 (~(elem!1 = s(s(elem!1)))),
% 0.60/0.89 inference(modus_ponens,[status(thm)],[449, 2753])).
% 0.60/0.89 tff(2755,plain,
% 0.60/0.89 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[522, 2750, 291])).
% 0.60/0.89 tff(2756,plain,
% 0.60/0.89 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[545, 2755, 2425])).
% 0.60/0.89 tff(2757,plain,
% 0.60/0.89 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[2682, 371, 254, 2756])).
% 0.60/0.89 tff(2758,plain,
% 0.60/0.89 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.60/0.89 inference(unit_resolution,[status(thm)],[963, 139, 177, 2757])).
% 0.60/0.89 tff(2759,assumption,(b(elem!1, s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.60/0.89 tff(2760,plain,
% 0.60/0.89 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.90 inference(rewrite,[status(thm)],[])).
% 0.60/0.90 tff(2761,plain,
% 0.60/0.90 (((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(elem!1))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.90 inference(rewrite,[status(thm)],[])).
% 0.60/0.90 tff(2762,plain,
% 0.60/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))))),
% 0.60/0.90 inference(monotonicity,[status(thm)],[2761])).
% 0.60/0.90 tff(2763,plain,
% 0.60/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.60/0.90 inference(transitivity,[status(thm)],[2762, 2760])).
% 0.60/0.90 tff(2764,plain,
% 0.60/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(elem!1)))))),
% 0.60/0.90 inference(quant_inst,[status(thm)],[])).
% 0.60/0.90 tff(2765,plain,
% 0.60/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.60/0.90 inference(modus_ponens,[status(thm)],[2764, 2763])).
% 0.60/0.90 tff(2766,plain,
% 0.60/0.90 (~b(elem!1, s(s(elem!1)))),
% 0.60/0.90 inference(unit_resolution,[status(thm)],[2765, 272, 2759, 1805])).
% 0.60/0.90 tff(2767,plain,
% 0.60/0.90 (r(elem!1, s(s(elem!1)))),
% 0.60/0.90 inference(unit_resolution,[status(thm)],[1045, 2766, 96])).
% 0.60/0.90 tff(2768,plain,
% 0.60/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 0.60/0.90 inference(rewrite,[status(thm)],[])).
% 0.60/0.90 tff(2769,plain,
% 0.60/0.90 (((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 0.60/0.90 inference(rewrite,[status(thm)],[])).
% 0.60/0.90 tff(2770,plain,
% 0.60/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))))),
% 0.60/0.90 inference(monotonicity,[status(thm)],[2769])).
% 0.60/0.90 tff(2771,plain,
% 0.60/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 0.60/0.90 inference(transitivity,[status(thm)],[2770, 2768])).
% 0.60/0.90 tff(2772,plain,
% 0.60/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(elem!1, s(elem!1))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(2773,plain,
% 0.70/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(elem!1), s(s(elem!1)))) | (~r(elem!1, s(elem!1)))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2772, 2771])).
% 0.70/0.90 tff(2774,plain,
% 0.70/0.90 (~r(elem!1, s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2773, 371, 2767, 902])).
% 0.70/0.90 tff(2775,plain,
% 0.70/0.90 (b(elem!1, s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[1574, 2774, 91])).
% 0.70/0.90 tff(2776,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2777,plain,
% 0.70/0.90 (((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2778,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2777])).
% 0.70/0.90 tff(2779,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(transitivity,[status(thm)],[2778, 2776])).
% 0.70/0.90 tff(2780,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(2781,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2780, 2779])).
% 0.70/0.90 tff(2782,plain,
% 0.70/0.90 ($false),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2781, 272, 2775, 514, 2759])).
% 0.70/0.90 tff(2783,plain,((~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (elem!1 = s(elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (elem!1 = s(s(elem!1))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.90 tff(2784,plain,
% 0.70/0.90 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2783, 2758, 1559, 902, 2754, 2750])).
% 0.70/0.90 tff(2785,plain,
% 0.70/0.90 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2179, 2784, 2710])).
% 0.70/0.90 tff(2786,plain,
% 0.70/0.90 (~r(elem!1, s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2718, 2785, 2748])).
% 0.70/0.90 tff(2787,plain,
% 0.70/0.90 (b(elem!1, s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2567, 2786, 2410])).
% 0.70/0.90 tff(2788,plain,
% 0.70/0.90 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2578, 2787, 291])).
% 0.70/0.90 tff(2789,plain,
% 0.70/0.90 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2586, 2788, 1])).
% 0.70/0.90 tff(2790,plain,
% 0.70/0.90 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2592, 2789])).
% 0.70/0.90 tff(2791,plain,
% 0.70/0.90 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2600, 2790, 1])).
% 0.70/0.90 tff(2792,plain,
% 0.70/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2793,plain,
% 0.70/0.90 (((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1))))))))) <=> ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2794,plain,
% 0.70/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2793])).
% 0.70/0.90 tff(2795,plain,
% 0.70/0.90 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))))),
% 0.70/0.90 inference(transitivity,[status(thm)],[2794, 2792])).
% 0.70/0.90 tff(2796,plain,
% 0.70/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(2797,plain,
% 0.70/0.90 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(elem!1), s(s(s(elem!1)))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2796, 2795])).
% 0.70/0.90 tff(2798,plain,
% 0.70/0.90 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2797, 371, 2748, 2791])).
% 0.70/0.90 tff(2799,plain,
% 0.70/0.90 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[695, 2798, 2403])).
% 0.70/0.90 tff(2800,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2801,plain,
% 0.70/0.90 (((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2802,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2801])).
% 0.70/0.90 tff(2803,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(transitivity,[status(thm)],[2802, 2800])).
% 0.70/0.90 tff(2804,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(2805,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2804, 2803])).
% 0.70/0.90 tff(2806,plain,
% 0.70/0.90 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2805, 272, 2799, 767])).
% 0.70/0.90 tff(2807,plain,
% 0.70/0.90 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2806, 2746])).
% 0.70/0.90 tff(2808,plain,
% 0.70/0.90 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2451, 2807, 2439])).
% 0.70/0.90 tff(2809,plain,
% 0.70/0.90 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2446, 2808, 1])).
% 0.70/0.90 tff(2810,plain,
% 0.70/0.90 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2578, 2570, 291])).
% 0.70/0.90 tff(2811,plain,
% 0.70/0.90 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2586, 2810, 1])).
% 0.70/0.90 tff(2812,plain,
% 0.70/0.90 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2592, 2811])).
% 0.70/0.90 tff(2813,plain,
% 0.70/0.90 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2600, 2812, 1])).
% 0.70/0.90 tff(2814,plain,
% 0.70/0.90 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2797, 371, 2748, 2813])).
% 0.70/0.90 tff(2815,plain,
% 0.70/0.90 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[695, 2814, 2403])).
% 0.70/0.90 tff(2816,plain,
% 0.70/0.90 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2805, 272, 2815, 767])).
% 0.70/0.90 tff(2817,plain,
% 0.70/0.90 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2816, 2746])).
% 0.70/0.90 tff(2818,plain,
% 0.70/0.90 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2451, 2817, 2439])).
% 0.70/0.90 tff(2819,plain,
% 0.70/0.90 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2446, 2818, 1])).
% 0.70/0.90 tff(2820,plain,
% 0.70/0.90 ((~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) <=> (~b(s(z), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2418])).
% 0.70/0.90 tff(2821,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2822,plain,
% 0.70/0.90 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(rewrite,[status(thm)],[])).
% 0.70/0.90 tff(2823,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2822])).
% 0.70/0.90 tff(2824,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(transitivity,[status(thm)],[2823, 2821])).
% 0.70/0.90 tff(2825,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.90 inference(quant_inst,[status(thm)],[])).
% 0.70/0.90 tff(2826,plain,
% 0.70/0.90 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2825, 2824])).
% 0.70/0.90 tff(2827,plain,
% 0.70/0.90 (~b(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2826, 272, 2815, 767])).
% 0.70/0.90 tff(2828,plain,
% 0.70/0.90 (~b(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2827, 2820])).
% 0.70/0.90 tff(2829,plain,
% 0.70/0.90 (r(s(z), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(unit_resolution,[status(thm)],[2485, 2828, 2429])).
% 0.70/0.90 tff(2830,plain,
% 0.70/0.90 (r(s(z), s(s(s(s(s(s(s(elem!1)))))))) <=> r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(symmetry,[status(thm)],[2430])).
% 0.70/0.90 tff(2831,assumption,(r(s(z), s(s(s(s(s(s(s(elem!1))))))))), introduced(assumption)).
% 0.70/0.90 tff(2832,plain,
% 0.70/0.90 (r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[2831, 2830])).
% 0.70/0.90 tff(2833,plain,
% 0.70/0.90 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(symmetry,[status(thm)],[2181])).
% 0.70/0.90 tff(2834,plain,
% 0.70/0.90 ((s(s(s(s(s(s(s(elem!1))))))) = z) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(transitivity,[status(thm)],[2432, 2833])).
% 0.70/0.90 tff(2835,plain,
% 0.70/0.90 ((~(s(s(s(s(s(s(s(elem!1))))))) = z)) <=> (~(elem!1 = s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.90 inference(monotonicity,[status(thm)],[2834])).
% 0.70/0.90 tff(2836,plain,
% 0.70/0.90 (~(elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.90 inference(modus_ponens,[status(thm)],[170, 2835])).
% 0.70/0.90 tff(2837,plain,
% 0.70/0.90 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2838,plain,
% 0.70/0.91 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2839,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[2838])).
% 0.70/0.91 tff(2840,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(transitivity,[status(thm)],[2839, 2837])).
% 0.70/0.91 tff(2841,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2842,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2841, 2840])).
% 0.70/0.91 tff(2843,plain,
% 0.70/0.91 (~b(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2842, 272, 2623, 2570])).
% 0.70/0.91 tff(2844,plain,
% 0.70/0.91 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2845,plain,
% 0.70/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2846,plain,
% 0.70/0.91 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2845, 2844])).
% 0.70/0.91 tff(2847,plain,
% 0.70/0.91 ((elem!1 = s(s(s(s(s(s(s(elem!1)))))))) | b(elem!1, s(s(s(s(s(s(s(elem!1)))))))) | r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2846, 139])).
% 0.70/0.91 tff(2848,plain,
% 0.70/0.91 (r(elem!1, s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2847, 2843, 2836])).
% 0.70/0.91 tff(2849,plain,
% 0.70/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2850,plain,
% 0.70/0.91 (((~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(elem!1)))) <=> ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2851,plain,
% 0.70/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[2850])).
% 0.70/0.91 tff(2852,plain,
% 0.70/0.91 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(transitivity,[status(thm)],[2851, 2849])).
% 0.70/0.91 tff(2853,plain,
% 0.70/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(elem!1))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2854,plain,
% 0.70/0.91 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1))))))))) | (~r(elem!1, s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2853, 2852])).
% 0.70/0.91 tff(2855,plain,
% 0.70/0.91 ((~r(elem!1, s(elem!1))) | (~r(s(elem!1), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2854, 371, 2848])).
% 0.70/0.91 tff(2856,plain,
% 0.70/0.91 (~r(elem!1, s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2855, 2832])).
% 0.70/0.91 tff(2857,plain,
% 0.70/0.91 (b(elem!1, s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1574, 2856, 91])).
% 0.70/0.91 tff(2858,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2859,plain,
% 0.70/0.91 (((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2860,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[2859])).
% 0.70/0.91 tff(2861,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.70/0.91 inference(transitivity,[status(thm)],[2860, 2858])).
% 0.70/0.91 tff(2862,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2863,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(elem!1, s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2862, 2861])).
% 0.70/0.91 tff(2864,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2863, 272, 2857, 514])).
% 0.70/0.91 tff(2865,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[545, 2864, 2425])).
% 0.70/0.91 tff(2866,plain,
% 0.70/0.91 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2682, 371, 254, 2865])).
% 0.70/0.91 tff(2867,plain,
% 0.70/0.91 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[963, 139, 177, 2866])).
% 0.70/0.91 tff(2868,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2869,plain,
% 0.70/0.91 (((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2870,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[2869])).
% 0.70/0.91 tff(2871,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(transitivity,[status(thm)],[2870, 2868])).
% 0.70/0.91 tff(2872,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2873,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2872, 2871])).
% 0.70/0.91 tff(2874,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2873, 272, 2623, 1983, 767, 2867])).
% 0.70/0.91 tff(2875,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (elem!1 = s(elem!1)) | (~r(s(z), s(s(s(s(s(s(s(elem!1))))))))) | (~(z = elem!1)) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(2876,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2875, 2829, 767, 177, 254, 514, 91, 1983, 1, 2570])).
% 0.70/0.91 tff(2877,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2537, 2876, 2508])).
% 0.70/0.91 tff(2878,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2668, 371, 2877, 2813, 2819])).
% 0.70/0.91 tff(2879,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (elem!1 = s(elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(2880,plain,
% 0.70/0.91 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2879, 2787, 177, 254, 2750, 1559, 767, 1, 291])).
% 0.70/0.91 tff(2881,plain,
% 0.70/0.91 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1766, 2880, 2404])).
% 0.70/0.91 tff(2882,plain,
% 0.70/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[549, 371, 254, 2756])).
% 0.70/0.91 tff(2883,plain,
% 0.70/0.91 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[611, 139, 1649, 2882])).
% 0.70/0.91 tff(2884,plain,
% 0.70/0.91 (~b(s(s(elem!1)), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1618, 2883, 2750])).
% 0.70/0.91 tff(2885,plain,
% 0.70/0.91 (r(s(s(elem!1)), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[660, 2884, 244])).
% 0.70/0.91 tff(2886,plain,
% 0.70/0.91 ($false),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2325, 371, 2885, 2881, 2809])).
% 0.70/0.91 tff(2887,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(elem!1), s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.91 tff(2888,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2887, 1, 177, 2745, 291, 244, 902])).
% 0.70/0.91 tff(2889,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1706, 2888, 2405])).
% 0.70/0.91 tff(2890,plain,
% 0.70/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2620, 1, 291, 2745, 2889, 177, 244])).
% 0.70/0.91 tff(2891,plain,
% 0.70/0.91 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[527, 2890, 2400])).
% 0.70/0.91 tff(2892,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[522, 2891, 291])).
% 0.70/0.91 tff(2893,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[545, 2892, 2425])).
% 0.70/0.91 tff(2894,plain,
% 0.70/0.91 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2682, 371, 2745, 2893])).
% 0.70/0.91 tff(2895,plain,
% 0.70/0.91 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[963, 139, 177, 2894])).
% 0.70/0.91 tff(2896,plain,
% 0.70/0.91 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2280, 2893, 2889])).
% 0.70/0.91 tff(2897,plain,
% 0.70/0.91 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1690, 2896, 2434])).
% 0.70/0.91 tff(2898,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2461, 2897, 291])).
% 0.70/0.91 tff(2899,plain,
% 0.70/0.91 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.91 inference(modus_ponens,[status(thm)],[2898, 2746])).
% 0.70/0.91 tff(2900,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2451, 2899, 2439])).
% 0.70/0.91 tff(2901,plain,
% 0.70/0.91 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2446, 2900, 1])).
% 0.70/0.91 tff(2902,plain,
% 0.70/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[1847, 1841, 1752])).
% 0.70/0.91 tff(2903,plain,
% 0.70/0.91 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[527, 2902, 2400])).
% 0.70/0.91 tff(2904,plain,
% 0.70/0.91 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2532, 2527, 1752])).
% 0.70/0.91 tff(2905,plain,
% 0.70/0.91 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.91 inference(unit_resolution,[status(thm)],[2524, 2904, 2507])).
% 0.70/0.91 tff(2906,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2907,plain,
% 0.70/0.91 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.91 inference(rewrite,[status(thm)],[])).
% 0.70/0.91 tff(2908,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.70/0.91 inference(monotonicity,[status(thm)],[2907])).
% 0.70/0.91 tff(2909,plain,
% 0.70/0.91 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.91 inference(transitivity,[status(thm)],[2908, 2906])).
% 0.70/0.91 tff(2910,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.70/0.91 inference(quant_inst,[status(thm)],[])).
% 0.70/0.91 tff(2911,plain,
% 0.70/0.91 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2910, 2909])).
% 0.70/0.92 tff(2912,plain,
% 0.70/0.92 (~b(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2911, 272, 514, 2511])).
% 0.70/0.92 tff(2913,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2912, 2583])).
% 0.70/0.92 tff(2914,plain,((~b(s(z), s(s(s(elem!1))))) | (~(z = elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2915,plain,
% 0.70/0.92 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2914, 2905, 2903, 1])).
% 0.70/0.92 tff(2916,plain,
% 0.70/0.92 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2592, 2915])).
% 0.70/0.92 tff(2917,plain,
% 0.70/0.92 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2600, 2916, 1])).
% 0.70/0.92 tff(2918,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2668, 371, 2527, 2917, 1841])).
% 0.70/0.92 tff(2919,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~(z = elem!1)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2920,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2919, 2901, 1, 2889])).
% 0.70/0.92 tff(2921,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2537, 2920, 2508])).
% 0.70/0.92 tff(2922,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2923,plain,
% 0.70/0.92 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))) <=> ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2924,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2923])).
% 0.70/0.92 tff(2925,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2924, 2922])).
% 0.70/0.92 tff(2926,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(2927,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2926, 2925])).
% 0.70/0.92 tff(2928,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2927, 272, 2623, 1677, 2570])).
% 0.70/0.92 tff(2929,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2930,plain,
% 0.70/0.92 (~b(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2929, 2921, 2897])).
% 0.70/0.92 tff(2931,plain,
% 0.70/0.92 (r(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2567, 2930, 2410])).
% 0.70/0.92 tff(2932,plain,
% 0.70/0.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2562, 2931, 2745])).
% 0.70/0.92 tff(2933,plain,
% 0.70/0.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2551, 2932, 2416])).
% 0.70/0.92 tff(2934,plain,
% 0.70/0.92 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2783, 2895, 1559, 902, 2754, 2891])).
% 0.70/0.92 tff(2935,plain,
% 0.70/0.92 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2179, 2934, 2710])).
% 0.70/0.92 tff(2936,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2718, 2931, 2935])).
% 0.70/0.92 tff(2937,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2524, 2936, 2507])).
% 0.70/0.92 tff(2938,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2519, 2937, 2933, 2895])).
% 0.70/0.92 tff(2939,plain,((~(z = elem!1)) | (~r(s(elem!1), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = s(elem!1)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2940,plain,
% 0.70/0.92 (~r(s(elem!1), s(s(elem!1)))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2939, 2744, 1, 291, 237, 177])).
% 0.70/0.92 tff(2941,plain,
% 0.70/0.92 (b(s(elem!1), s(s(elem!1)))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[635, 2940, 624])).
% 0.70/0.92 tff(2942,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2943,plain,
% 0.70/0.92 (((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2944,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2943])).
% 0.70/0.92 tff(2945,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2944, 2942])).
% 0.70/0.92 tff(2946,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(2947,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2946, 2945])).
% 0.70/0.92 tff(2948,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2947, 272, 291, 2941, 2737, 2741])).
% 0.70/0.92 tff(2949,plain,((~r(s(s(elem!1)), elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~(z = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2950,plain,
% 0.70/0.92 (~r(s(s(elem!1)), elem!1)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2949, 291, 221, 177, 1])).
% 0.70/0.92 tff(2951,plain,
% 0.70/0.92 (b(s(s(elem!1)), elem!1)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[843, 2950, 231])).
% 0.70/0.92 tff(2952,plain,
% 0.70/0.92 (~b(s(s(elem!1)), s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[1232, 272, 2951, 291])).
% 0.70/0.92 tff(2953,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[660, 2952, 237])).
% 0.70/0.92 tff(2954,plain,
% 0.70/0.92 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[1394, 2953, 1649, 2951, 2400, 291])).
% 0.70/0.92 tff(2955,plain,
% 0.70/0.92 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[545, 2954, 221])).
% 0.70/0.92 tff(2956,assumption,(elem!1 = s(s(s(elem!1)))), introduced(assumption)).
% 0.70/0.92 tff(2957,plain,
% 0.70/0.92 (s(elem!1) = s(s(s(s(elem!1))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2956])).
% 0.70/0.92 tff(2958,plain,
% 0.70/0.92 (s(s(elem!1)) = s(s(s(s(s(elem!1)))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2957])).
% 0.70/0.92 tff(2959,plain,
% 0.70/0.92 (s(s(s(s(s(elem!1))))) = s(s(elem!1))),
% 0.70/0.92 inference(symmetry,[status(thm)],[2958])).
% 0.70/0.92 tff(2960,plain,
% 0.70/0.92 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2959])).
% 0.70/0.92 tff(2961,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2401, 2960])).
% 0.70/0.92 tff(2962,plain,((~(elem!1 = s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2963,plain,
% 0.70/0.92 (~(elem!1 = s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2962, 2384])).
% 0.70/0.92 tff(2964,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), s(elem!1))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2396])).
% 0.70/0.92 tff(2965,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(elem!1)) <=> r(s(s(elem!1)), s(z))),
% 0.70/0.92 inference(symmetry,[status(thm)],[2964])).
% 0.70/0.92 tff(2966,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(z))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2953, 2965])).
% 0.70/0.92 tff(2967,plain,
% 0.70/0.92 (s(s(s(elem!1))) = s(s(elem!1))),
% 0.70/0.92 inference(symmetry,[status(thm)],[2411])).
% 0.70/0.92 tff(2968,plain,
% 0.70/0.92 (s(s(s(s(elem!1)))) = s(s(s(elem!1)))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2967])).
% 0.70/0.92 tff(2969,plain,
% 0.70/0.92 (s(s(s(s(s(elem!1))))) = s(s(s(s(elem!1))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2968])).
% 0.70/0.92 tff(2970,plain,
% 0.70/0.92 (s(s(s(s(s(elem!1))))) = s(s(s(elem!1)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2969, 2968])).
% 0.70/0.92 tff(2971,plain,
% 0.70/0.92 (s(s(s(s(s(s(elem!1)))))) = s(s(s(s(elem!1))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2970])).
% 0.70/0.92 tff(2972,plain,
% 0.70/0.92 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2971, 2968])).
% 0.70/0.92 tff(2973,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2401, 2972])).
% 0.70/0.92 tff(2974,plain,((~(s(s(elem!1)) = s(s(s(elem!1))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2975,plain,
% 0.70/0.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2974, 2384])).
% 0.70/0.92 tff(2976,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2977,plain,
% 0.70/0.92 (((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))) <=> ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2978,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2977])).
% 0.70/0.92 tff(2979,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1))))))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2978, 2976])).
% 0.70/0.92 tff(2980,plain,
% 0.70/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(2981,plain,
% 0.70/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2980, 2979])).
% 0.70/0.92 tff(2982,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2981, 371, 2553, 2596, 943])).
% 0.70/0.92 tff(2983,plain,((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2984,plain,
% 0.70/0.92 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2983, 2812, 943])).
% 0.70/0.92 tff(2985,plain,
% 0.70/0.92 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2551, 2984, 2645])).
% 0.70/0.92 tff(2986,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2987,plain,
% 0.70/0.92 (((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2988,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2987])).
% 0.70/0.92 tff(2989,plain,
% 0.70/0.92 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2988, 2986])).
% 0.70/0.92 tff(2990,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(2991,plain,
% 0.70/0.92 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[2990, 2989])).
% 0.70/0.92 tff(2992,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2991, 272, 864, 2570, 2985])).
% 0.70/0.92 tff(2993,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(elem!1)), elem!1)) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(z))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(2994,plain,
% 0.70/0.92 (~b(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2993, 2951, 2975, 2966, 1, 291])).
% 0.70/0.92 tff(2995,plain,
% 0.70/0.92 (r(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2567, 2994, 2963])).
% 0.70/0.92 tff(2996,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2997,plain,
% 0.70/0.92 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.92 inference(rewrite,[status(thm)],[])).
% 0.70/0.92 tff(2998,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2997])).
% 0.70/0.92 tff(2999,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.92 inference(transitivity,[status(thm)],[2998, 2996])).
% 0.70/0.92 tff(3000,plain,
% 0.70/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.70/0.92 inference(quant_inst,[status(thm)],[])).
% 0.70/0.92 tff(3001,plain,
% 0.70/0.92 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[3000, 2999])).
% 0.70/0.92 tff(3002,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3001, 371, 552, 2526, 2554])).
% 0.70/0.92 tff(3003,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(3004,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3003, 2995, 2955])).
% 0.70/0.92 tff(3005,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2524, 3004, 2384])).
% 0.70/0.92 tff(3006,plain,
% 0.70/0.92 ((~(s(s(s(s(s(s(elem!1)))))) = elem!1)) <=> (~(elem!1 = s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2172])).
% 0.70/0.92 tff(3007,plain,
% 0.70/0.92 (~(elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[221, 3006])).
% 0.70/0.92 tff(3008,plain,
% 0.70/0.92 (~(s(s(elem!1)) = s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2974, 2401])).
% 0.70/0.92 tff(3009,plain,
% 0.70/0.92 (~(elem!1 = s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2962, 2401])).
% 0.70/0.92 tff(3010,plain,
% 0.70/0.92 (~(s(s(elem!1)) = s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[98, 96])).
% 0.70/0.92 tff(3011,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[660, 1363, 3010])).
% 0.70/0.92 tff(3012,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(z))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[3011, 2965])).
% 0.70/0.92 tff(3013,plain,
% 0.70/0.92 (~b(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2993, 864, 3008, 3012, 1, 291])).
% 0.70/0.92 tff(3014,plain,
% 0.70/0.92 (r(elem!1, s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2567, 3013, 3009])).
% 0.70/0.92 tff(3015,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3003, 3014, 552])).
% 0.70/0.92 tff(3016,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2524, 3015, 2401])).
% 0.70/0.92 tff(3017,plain,
% 0.70/0.92 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2504, 371, 3011, 1842])).
% 0.70/0.92 tff(3018,plain,
% 0.70/0.92 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[963, 139, 177, 3017])).
% 0.70/0.92 tff(3019,plain,
% 0.70/0.92 (~b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2519, 3018, 3016])).
% 0.70/0.92 tff(3020,plain,
% 0.70/0.92 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2551, 3019, 3008])).
% 0.70/0.92 tff(3021,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.92 inference(monotonicity,[status(thm)],[2396])).
% 0.70/0.92 tff(3022,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[1847, 1752, 1842])).
% 0.70/0.92 tff(3023,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2446, 3022, 1])).
% 0.70/0.92 tff(3024,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(z)) | r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2451, 1643])).
% 0.70/0.92 tff(3025,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3024, 3023])).
% 0.70/0.92 tff(3026,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.92 inference(modus_ponens,[status(thm)],[3025, 3021])).
% 0.70/0.92 tff(3027,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[1690, 2281, 2434])).
% 0.70/0.92 tff(3028,plain,
% 0.70/0.92 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2461, 3027, 291])).
% 0.70/0.92 tff(3029,plain,
% 0.70/0.92 ($false),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3028, 3026])).
% 0.70/0.92 tff(3030,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~(z = elem!1)) | (~b(s(elem!1), elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.92 tff(3031,plain,
% 0.70/0.92 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[3030, 1842, 291, 1, 552])).
% 0.70/0.92 tff(3032,plain,
% 0.70/0.92 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[1706, 3031, 2405])).
% 0.70/0.92 tff(3033,plain,
% 0.70/0.92 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2631, 3032, 3016])).
% 0.70/0.92 tff(3034,plain,
% 0.70/0.92 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.92 inference(unit_resolution,[status(thm)],[2537, 3033, 2508])).
% 0.70/0.92 tff(3035,plain,
% 0.70/0.92 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(3036,plain,
% 0.70/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(3037,plain,
% 0.70/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[3036, 3035])).
% 0.70/0.93 tff(3038,plain,
% 0.70/0.93 ($false),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3037, 371, 2527, 1753, 2553])).
% 0.70/0.93 tff(3039,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))) | (~r(s(s(elem!1)), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.93 tff(3040,plain,
% 0.70/0.93 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3039, 3034, 3020])).
% 0.70/0.93 tff(3041,assumption,(~(elem!1 = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.70/0.93 tff(3042,plain,
% 0.70/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1390, 371, 3011, 1842])).
% 0.70/0.93 tff(3043,plain,
% 0.70/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[611, 139, 1649, 3042])).
% 0.70/0.93 tff(3044,plain,
% 0.70/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(3045,plain,
% 0.70/0.93 (((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1))))) <=> ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(3046,plain,
% 0.70/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[3045])).
% 0.70/0.93 tff(3047,plain,
% 0.70/0.93 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.93 inference(transitivity,[status(thm)],[3046, 3044])).
% 0.70/0.93 tff(3048,plain,
% 0.70/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))) | (~r(elem!1, s(s(elem!1)))))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(3049,plain,
% 0.70/0.93 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[3048, 3047])).
% 0.70/0.93 tff(3050,plain,
% 0.70/0.93 (~r(elem!1, s(s(elem!1)))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3049, 371, 3014, 3020])).
% 0.70/0.93 tff(3051,plain,
% 0.70/0.93 (b(elem!1, s(s(elem!1)))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1045, 3050, 96])).
% 0.70/0.93 tff(3052,plain,
% 0.70/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(3053,plain,
% 0.70/0.93 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.93 inference(rewrite,[status(thm)],[])).
% 0.70/0.93 tff(3054,plain,
% 0.70/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))))),
% 0.70/0.93 inference(monotonicity,[status(thm)],[3053])).
% 0.70/0.93 tff(3055,plain,
% 0.70/0.93 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))))),
% 0.70/0.93 inference(transitivity,[status(thm)],[3054, 3052])).
% 0.70/0.93 tff(3056,plain,
% 0.70/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.70/0.93 inference(quant_inst,[status(thm)],[])).
% 0.70/0.93 tff(3057,plain,
% 0.70/0.93 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))),
% 0.70/0.93 inference(modus_ponens,[status(thm)],[3056, 3055])).
% 0.70/0.93 tff(3058,plain,
% 0.70/0.93 (~b(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3057, 272, 3051, 3016, 3043])).
% 0.70/0.93 tff(3059,plain,
% 0.70/0.93 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2179, 3058, 3041])).
% 0.70/0.93 tff(3060,plain,
% 0.70/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2718, 2554, 2201])).
% 0.70/0.93 tff(3061,plain,
% 0.70/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2524, 3060, 2401])).
% 0.70/0.93 tff(3062,plain,
% 0.70/0.93 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2631, 3061, 767])).
% 0.70/0.93 tff(3063,plain,
% 0.70/0.93 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2537, 3062, 2510])).
% 0.70/0.93 tff(3064,plain,
% 0.70/0.93 ($false),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2639, 371, 3063, 752, 2554])).
% 0.70/0.93 tff(3065,plain,((~r(elem!1, s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.93 tff(3066,plain,
% 0.70/0.93 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3065, 3032, 3014, 2401, 2508, 3059])).
% 0.70/0.93 tff(3067,plain,
% 0.70/0.93 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1690, 3066, 2434])).
% 0.70/0.93 tff(3068,plain,
% 0.70/0.93 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1991, 3067, 864])).
% 0.70/0.93 tff(3069,plain,
% 0.70/0.93 ($false),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1766, 3068, 3040, 2404])).
% 0.70/0.93 tff(3070,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(elem!1)), elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~b(s(elem!1), elem!1)) | (~(z = elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (elem!1 = s(s(s(s(s(s(elem!1))))))) | (elem!1 = s(s(elem!1))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.93 tff(3071,plain,
% 0.70/0.93 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[3070, 2951, 2384, 291, 1, 2955, 3007, 236, 177])).
% 0.70/0.93 tff(3072,plain,
% 0.70/0.93 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[527, 3071, 2400])).
% 0.70/0.93 tff(3073,plain,
% 0.70/0.93 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2914, 3072, 3005, 1])).
% 0.70/0.93 tff(3074,plain,
% 0.70/0.93 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2592, 3073])).
% 0.70/0.93 tff(3075,plain,
% 0.70/0.93 (~r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2983, 3074, 2966])).
% 0.70/0.93 tff(3076,plain,
% 0.70/0.93 (b(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2551, 3075, 2975])).
% 0.70/0.93 tff(3077,plain,
% 0.70/0.93 (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2519, 3076, 3005])).
% 0.70/0.93 tff(3078,plain,
% 0.70/0.93 (r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[963, 139, 177, 3077])).
% 0.70/0.93 tff(3079,plain,
% 0.70/0.93 (~(elem!1 = s(elem!1))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[1558, 247])).
% 0.70/0.93 tff(3080,plain,
% 0.70/0.93 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.93 inference(unit_resolution,[status(thm)],[2600, 3074, 1])).
% 0.70/0.93 tff(3081,plain,
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% 0.70/0.93 inference(rewrite,[status(thm)],[])).
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% 0.70/0.93 inference(monotonicity,[status(thm)],[3082])).
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% 0.70/0.93 inference(transitivity,[status(thm)],[3083, 3081])).
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% 0.70/0.93 inference(modus_ponens,[status(thm)],[3085, 3084])).
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% 0.70/0.93 inference(symmetry,[status(thm)],[3021])).
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% 0.70/0.93 inference(monotonicity,[status(thm)],[3091])).
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% 0.70/0.93 inference(unit_resolution,[status(thm)],[2537, 3097, 2510])).
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% 0.70/0.93 inference(unit_resolution,[status(thm)],[2668, 371, 3098, 2602])).
% 0.70/0.93 tff(3100,plain,
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% 0.70/0.93 inference(unit_resolution,[status(thm)],[2446, 3099, 1])).
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% 0.70/0.93 inference(unit_resolution,[status(thm)],[3024, 3100])).
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% 0.70/0.93 tff(3104,plain,
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% 0.70/0.93 tff(3109,plain,
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% 0.70/0.93 inference(transitivity,[status(thm)],[3133, 3131])).
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% 0.70/0.94 tff(3139,plain,
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% 0.70/0.94 tff(3146,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3147,plain,
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% 0.70/0.94 tff(3148,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3149,plain,
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% 0.70/0.94 inference(unit_resolution,[status(thm)],[3148, 3140, 2510, 2404, 2526, 944])).
% 0.70/0.94 tff(3150,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1706, 3149, 2405])).
% 0.70/0.94 tff(3151,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3152,plain,
% 0.70/0.94 (((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3153,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3152])).
% 0.70/0.94 tff(3154,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.70/0.94 inference(transitivity,[status(thm)],[3153, 3151])).
% 0.70/0.94 tff(3155,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))))),
% 0.70/0.94 inference(quant_inst,[status(thm)],[])).
% 0.70/0.94 tff(3156,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3155, 3154])).
% 0.70/0.94 tff(3157,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3156, 272, 2059, 2509, 2582])).
% 0.70/0.94 tff(3158,plain,((~b(s(s(elem!1)), s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (~b(s(z), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3159,plain,
% 0.70/0.94 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3158, 3140, 2059])).
% 0.70/0.94 tff(3160,plain,
% 0.70/0.94 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2592, 3159])).
% 0.70/0.94 tff(3161,plain,
% 0.70/0.94 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2600, 3160, 1])).
% 0.70/0.94 tff(3162,plain,
% 0.70/0.94 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2797, 371, 2526, 3161])).
% 0.70/0.94 tff(3163,plain,
% 0.70/0.94 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[695, 3162, 2403])).
% 0.70/0.94 tff(3164,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1675, 272, 643, 3163, 3150])).
% 0.70/0.94 tff(3165,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3164, 3092])).
% 0.70/0.94 tff(3166,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1685, 3150, 504])).
% 0.70/0.94 tff(3167,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1690, 3166, 2434])).
% 0.70/0.94 tff(3168,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1694, 371, 637, 3167])).
% 0.70/0.94 tff(3169,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2446, 3168, 1])).
% 0.70/0.94 tff(3170,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3024, 3169])).
% 0.70/0.94 tff(3171,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3170, 3165])).
% 0.70/0.94 tff(3172,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~(z = elem!1)) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3173,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3172, 3130, 637, 643, 504, 2508, 1, 2059, 3008])).
% 0.70/0.94 tff(3174,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2524, 3173, 2401])).
% 0.70/0.94 tff(3175,plain,
% 0.70/0.94 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2914, 3174, 514, 1])).
% 0.70/0.94 tff(3176,plain,
% 0.70/0.94 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2592, 3175])).
% 0.70/0.94 tff(3177,plain,
% 0.70/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3178,plain,
% 0.70/0.94 (((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3179,plain,
% 0.70/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3178])).
% 0.70/0.94 tff(3180,plain,
% 0.70/0.94 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1))))))),
% 0.70/0.94 inference(transitivity,[status(thm)],[3179, 3177])).
% 0.70/0.94 tff(3181,plain,
% 0.70/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)))),
% 0.70/0.94 inference(quant_inst,[status(thm)],[])).
% 0.70/0.94 tff(3182,plain,
% 0.70/0.94 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(elem!1, s(s(s(elem!1)))))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3181, 3180])).
% 0.70/0.94 tff(3183,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3182, 371, 1101, 2554, 2596])).
% 0.70/0.94 tff(3184,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3185,plain,
% 0.70/0.94 (~r(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3184, 3176, 3128])).
% 0.70/0.94 tff(3186,plain,
% 0.70/0.94 (b(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2567, 3185, 3009])).
% 0.70/0.94 tff(3187,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2618, 272, 504, 3174, 3186])).
% 0.70/0.94 tff(3188,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~(z = elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) | (~r(s(elem!1), elem!1)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (~b(s(s(elem!1)), s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3189,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3188, 3127, 1, 2384, 3112, 3124, 3122, 177, 3114])).
% 0.70/0.94 tff(3190,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[527, 3189, 2400])).
% 0.70/0.94 tff(3191,plain,
% 0.70/0.94 (~r(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3184, 2554, 1101])).
% 0.70/0.94 tff(3192,plain,
% 0.70/0.94 (b(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2592, 3191])).
% 0.70/0.94 tff(3193,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3158, 2647, 3192, 2059])).
% 0.70/0.94 tff(3194,plain,((~r(elem!1, s(s(s(elem!1))))) | (~b(s(z), s(s(elem!1)))) | (s(s(elem!1)) = s(s(s(elem!1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3195,plain,
% 0.70/0.94 (~r(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3194, 3122, 2975, 254, 3125])).
% 0.70/0.94 tff(3196,plain,
% 0.70/0.94 (b(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2567, 3195, 2963])).
% 0.70/0.94 tff(3197,plain,
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% 0.70/0.94 inference(unit_resolution,[status(thm)],[2618, 272, 504, 2511, 2570])).
% 0.70/0.94 tff(3198,plain,((~b(elem!1, s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3199,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3198, 3196, 3127])).
% 0.70/0.94 tff(3200,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2524, 3199, 2384])).
% 0.70/0.94 tff(3201,plain,
% 0.70/0.94 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3172, 3200, 3112, 3124, 3127, 2508, 1, 3122, 2975])).
% 0.70/0.94 tff(3202,plain,
% 0.70/0.94 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[963, 139, 177, 3201])).
% 0.70/0.94 tff(3203,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1821, 254, 2404, 3202, 2434, 3127])).
% 0.70/0.94 tff(3204,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1706, 3203, 2405])).
% 0.70/0.94 tff(3205,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1847, 3204, 3190])).
% 0.70/0.94 tff(3206,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2446, 3205, 1])).
% 0.70/0.94 tff(3207,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
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% 0.70/0.94 tff(3208,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3207, 3021])).
% 0.70/0.94 tff(3209,plain,
% 0.70/0.94 (~r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2610, 3200, 3190])).
% 0.70/0.94 tff(3210,plain,
% 0.70/0.94 (~r(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2600, 3209, 1])).
% 0.70/0.94 tff(3211,plain,
% 0.70/0.94 (b(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2592, 3210])).
% 0.70/0.94 tff(3212,plain,
% 0.70/0.94 (b(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2586, 3211, 1])).
% 0.70/0.94 tff(3213,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2532, 3204, 3200])).
% 0.70/0.94 tff(3214,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2537, 3213, 2508])).
% 0.70/0.94 tff(3215,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3216,plain,
% 0.70/0.94 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3217,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3216])).
% 0.70/0.94 tff(3218,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.94 inference(transitivity,[status(thm)],[3217, 3215])).
% 0.70/0.94 tff(3219,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.94 inference(quant_inst,[status(thm)],[])).
% 0.70/0.94 tff(3220,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3219, 3218])).
% 0.70/0.94 tff(3221,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3220, 272, 3124, 3214, 3212, 3208])).
% 0.70/0.94 tff(3222,plain,((~r(s(s(elem!1)), elem!1)) | (~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3223,plain,
% 0.70/0.94 (~r(s(s(elem!1)), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3222, 2394, 2393, 221])).
% 0.70/0.94 tff(3224,plain,
% 0.70/0.94 (b(s(s(elem!1)), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[843, 3223, 231])).
% 0.70/0.94 tff(3225,plain,
% 0.70/0.94 (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2383, 1696])).
% 0.70/0.94 tff(3226,plain,
% 0.70/0.94 (~(elem!1 = s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2962, 3225])).
% 0.70/0.94 tff(3227,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[527, 1156, 2400])).
% 0.70/0.94 tff(3228,plain,
% 0.70/0.94 (~b(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2914, 2511, 514, 1])).
% 0.70/0.94 tff(3229,plain,
% 0.70/0.94 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2592, 3228])).
% 0.70/0.94 tff(3230,plain,
% 0.70/0.94 (r(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2600, 3229, 1])).
% 0.70/0.94 tff(3231,assumption,(~(elem!1 = s(s(s(elem!1))))), introduced(assumption)).
% 0.70/0.94 tff(3232,plain,
% 0.70/0.94 (~r(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3184, 3229, 1101])).
% 0.70/0.94 tff(3233,plain,
% 0.70/0.94 (b(elem!1, s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2567, 3232, 3231])).
% 0.70/0.94 tff(3234,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2929, 2623, 2570])).
% 0.70/0.94 tff(3235,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1690, 3234, 1652])).
% 0.70/0.94 tff(3236,assumption,(~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.70/0.94 tff(3237,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2631, 2623, 2511])).
% 0.70/0.94 tff(3238,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1706, 3237, 3236])).
% 0.70/0.94 tff(3239,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2280, 3238, 3235, 552])).
% 0.70/0.94 tff(3240,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))) | (~b(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3241,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3240, 3233, 2405, 2434, 552, 2511])).
% 0.70/0.94 tff(3242,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2537, 3241, 2510])).
% 0.70/0.94 tff(3243,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2668, 371, 3242, 3230])).
% 0.70/0.94 tff(3244,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2446, 3243, 1])).
% 0.70/0.94 tff(3245,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3024, 3244])).
% 0.70/0.94 tff(3246,plain,
% 0.70/0.94 (b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3245, 3021])).
% 0.70/0.94 tff(3247,plain,
% 0.70/0.94 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2352, 272, 514, 3246])).
% 0.70/0.94 tff(3248,plain,
% 0.70/0.94 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[1706, 3247, 2405])).
% 0.70/0.94 tff(3249,plain,
% 0.70/0.94 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[2280, 3248, 552])).
% 0.70/0.94 tff(3250,plain,
% 0.70/0.94 (s(s(z)) = s(s(elem!1))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[2396])).
% 0.70/0.94 tff(3251,plain,
% 0.70/0.94 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3250])).
% 0.70/0.94 tff(3252,plain,
% 0.70/0.94 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3250, 3251])).
% 0.70/0.94 tff(3253,plain,
% 0.70/0.94 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 0.70/0.94 inference(monotonicity,[status(thm)],[1])).
% 0.70/0.94 tff(3254,plain,
% 0.70/0.94 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 0.70/0.94 inference(symmetry,[status(thm)],[3253])).
% 0.70/0.94 tff(3255,plain,
% 0.70/0.94 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3250])).
% 0.70/0.94 tff(3256,plain,
% 0.70/0.94 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 0.70/0.94 inference(symmetry,[status(thm)],[3255])).
% 0.70/0.94 tff(3257,plain,
% 0.70/0.94 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 0.70/0.94 inference(transitivity,[status(thm)],[3256, 3254])).
% 0.70/0.94 tff(3258,plain,
% 0.70/0.94 (b(s(s(z)), z)),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[864, 3257])).
% 0.70/0.94 tff(3259,plain,
% 0.70/0.94 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[1])).
% 0.70/0.94 tff(3260,plain,
% 0.70/0.94 (b(elem!1, s(s(s(z)))) <=> b(z, s(s(s(z))))),
% 0.70/0.94 inference(symmetry,[status(thm)],[3259])).
% 0.70/0.94 tff(3261,plain,
% 0.70/0.94 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.70/0.94 inference(symmetry,[status(thm)],[3251])).
% 0.70/0.94 tff(3262,plain,
% 0.70/0.94 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3261])).
% 0.70/0.94 tff(3263,plain,
% 0.70/0.94 (b(elem!1, s(s(s(elem!1)))) <=> b(z, s(s(s(z))))),
% 0.70/0.94 inference(transitivity,[status(thm)],[3262, 3260])).
% 0.70/0.94 tff(3264,plain,
% 0.70/0.94 (b(z, s(s(s(z))))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3233, 3263])).
% 0.70/0.94 tff(3265,assumption,(b(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.70/0.94 tff(3266,assumption,(b(z, s(s(s(z))))), introduced(assumption)).
% 0.70/0.94 tff(3267,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3268,plain,
% 0.70/0.94 (((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/0.94 inference(rewrite,[status(thm)],[])).
% 0.70/0.94 tff(3269,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.70/0.94 inference(monotonicity,[status(thm)],[3268])).
% 0.70/0.94 tff(3270,plain,
% 0.70/0.94 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/0.94 inference(transitivity,[status(thm)],[3269, 3267])).
% 0.70/0.94 tff(3271,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), z)))),
% 0.70/0.94 inference(quant_inst,[status(thm)],[])).
% 0.70/0.94 tff(3272,plain,
% 0.70/0.94 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.70/0.94 inference(modus_ponens,[status(thm)],[3271, 3270])).
% 0.70/0.94 tff(3273,plain,
% 0.70/0.94 ($false),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3272, 272, 779, 3266, 3265])).
% 0.70/0.94 tff(3274,plain,((~b(z, s(s(s(z))))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.94 tff(3275,plain,
% 0.70/0.94 (~b(s(s(z)), s(s(s(z))))),
% 0.70/0.94 inference(unit_resolution,[status(thm)],[3274, 3264, 3258])).
% 0.70/0.94 tff(3276,assumption,(s(s(z)) = s(s(s(z)))), introduced(assumption)).
% 0.70/0.95 tff(3277,plain,
% 0.70/0.95 ((s(z) = s(s(z))) <=> (s(z) = s(s(s(z))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3276])).
% 0.70/0.95 tff(3278,plain,
% 0.70/0.95 ((s(z) = s(s(s(z)))) <=> (s(z) = s(s(z)))),
% 0.70/0.95 inference(symmetry,[status(thm)],[3277])).
% 0.70/0.95 tff(3279,plain,
% 0.70/0.95 (inj_0(s(s(z))) = inj_0(s(s(s(z))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3276])).
% 0.70/0.95 tff(3280,plain,
% 0.70/0.95 (s(z) = s(s(s(z)))),
% 0.70/0.95 inference(transitivity,[status(thm)],[213, 3279, 190, 3276])).
% 0.70/0.95 tff(3281,plain,
% 0.70/0.95 (s(z) = s(s(z))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3280, 3278])).
% 0.70/0.95 tff(3282,plain,
% 0.70/0.95 ($false),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[353, 3281])).
% 0.70/0.95 tff(3283,plain,(~(s(s(z)) = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.95 tff(3284,plain,
% 0.70/0.95 (((~![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)))))),
% 0.70/0.95 inference(rewrite,[status(thm)],[])).
% 0.70/0.95 tff(3285,plain,
% 0.70/0.95 ((~![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)))))),
% 0.70/0.95 inference(quant_inst,[status(thm)],[])).
% 0.70/0.95 tff(3286,plain,
% 0.70/0.95 ((~![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))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3285, 3284])).
% 0.70/0.95 tff(3287,plain,
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3286, 139])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3287, 3283])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3288, 3275])).
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% 0.70/0.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3289, 3252])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3037, 371, 3242, 3290])).
% 0.70/0.95 tff(3292,plain,
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[1766, 3291, 2404])).
% 0.70/0.95 tff(3293,plain,
% 0.70/0.95 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[1991, 3292, 864])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[1690, 3293, 3249, 2434])).
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% 0.70/0.95 tff(3296,plain,
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3295, 552, 864, 3227, 1, 2508, 3226, 3128])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[2524, 3296, 3225])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3003, 3297, 552])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[2567, 3298, 3226])).
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% 0.70/0.95 tff(3302,plain,
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[1706, 3302, 2405])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[695, 691, 2403])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[2805, 272, 3304, 3303])).
% 0.70/0.95 tff(3306,plain,
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% 0.70/0.95 inference(modus_ponens,[status(thm)],[3299, 3263])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3274, 3307, 3258])).
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% 0.70/0.95 inference(modus_ponens,[status(thm)],[3309, 3252])).
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% 0.70/0.95 inference(monotonicity,[status(thm)],[3312])).
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% 0.70/0.95 inference(modus_ponens,[status(thm)],[3315, 3314])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[3316, 371, 3297, 3310])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[611, 139, 1649, 3317])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[1618, 3318, 3227])).
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% 0.70/0.95 inference(unit_resolution,[status(thm)],[660, 3319, 244])).
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% 0.70/0.95 (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2325, 371, 3320, 3306])).
% 0.70/0.95 tff(3322,plain,
% 0.70/0.95 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3136, 371, 3297, 3310])).
% 0.70/0.95 tff(3323,plain,
% 0.70/0.95 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[963, 139, 177, 3322])).
% 0.70/0.95 tff(3324,plain,
% 0.70/0.95 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
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% 0.70/0.95 inference(symmetry,[status(thm)],[3331])).
% 0.70/0.95 tff(3333,plain,
% 0.70/0.95 (b(elem!1, s(s(s(elem!1)))) <=> b(elem!1, s(s(s(z))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3332])).
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% 0.70/0.95 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(z))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[2394])).
% 0.70/0.95 tff(3336,plain,
% 0.70/0.95 (b(z, s(s(s(z)))) <=> b(elem!1, s(s(s(elem!1))))),
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% 0.70/0.95 (r(elem!1, s(s(s(elem!1)))) <=> r(z, s(s(s(elem!1))))),
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% 0.70/0.95 (r(elem!1, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
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% 0.70/0.95 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(z))))),
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% 0.70/0.95 (r(z, s(s(s(z)))) <=> r(z, s(s(s(elem!1))))),
% 0.70/0.95 inference(transitivity,[status(thm)],[3363, 3362, 3361])).
% 0.70/0.95 tff(3365,plain,
% 0.70/0.95 (r(z, s(s(s(elem!1))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[1521, 3364])).
% 0.70/0.95 tff(3366,assumption,(r(z, s(s(s(elem!1))))), introduced(assumption)).
% 0.70/0.95 tff(3367,plain,
% 0.70/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 0.70/0.95 inference(rewrite,[status(thm)],[])).
% 0.70/0.95 tff(3368,plain,
% 0.70/0.95 (((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z))) <=> ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 0.70/0.95 inference(rewrite,[status(thm)],[])).
% 0.70/0.95 tff(3369,plain,
% 0.70/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3368])).
% 0.70/0.95 tff(3370,plain,
% 0.70/0.95 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1))))))),
% 0.70/0.95 inference(transitivity,[status(thm)],[3369, 3367])).
% 0.70/0.95 tff(3371,plain,
% 0.70/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)))),
% 0.70/0.95 inference(quant_inst,[status(thm)],[])).
% 0.70/0.95 tff(3372,plain,
% 0.70/0.95 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~r(z, s(s(s(elem!1)))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3371, 3370])).
% 0.70/0.95 tff(3373,plain,
% 0.70/0.95 ($false),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3372, 371, 672, 2596, 3366])).
% 0.70/0.95 tff(3374,plain,((~r(s(z), s(s(s(elem!1))))) | (~r(s(z), z)) | (~r(z, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.95 tff(3375,plain,
% 0.70/0.95 (~r(s(z), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3374, 3365, 672])).
% 0.70/0.95 tff(3376,plain,
% 0.70/0.95 (b(s(z), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2592, 3375])).
% 0.70/0.95 tff(3377,plain,
% 0.70/0.95 (b(s(elem!1), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2586, 3376, 1])).
% 0.70/0.95 tff(3378,plain,
% 0.70/0.95 (r(z, s(s(s(z)))) <=> r(elem!1, s(s(s(elem!1))))),
% 0.70/0.95 inference(transitivity,[status(thm)],[3363, 3362])).
% 0.70/0.95 tff(3379,plain,
% 0.70/0.95 (r(elem!1, s(s(s(elem!1))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[1521, 3378])).
% 0.70/0.95 tff(3380,plain,
% 0.70/0.95 ($false),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2639, 371, 2527, 752, 2554])).
% 0.70/0.95 tff(3381,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(elem!1, s(s(s(elem!1)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.95 tff(3382,plain,
% 0.70/0.95 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3381, 3379, 752])).
% 0.70/0.95 tff(3383,plain,
% 0.70/0.95 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2537, 3382, 2510])).
% 0.70/0.95 tff(3384,plain,
% 0.70/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.95 inference(rewrite,[status(thm)],[])).
% 0.70/0.95 tff(3385,plain,
% 0.70/0.95 (((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.95 inference(rewrite,[status(thm)],[])).
% 0.70/0.95 tff(3386,plain,
% 0.70/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3385])).
% 0.70/0.95 tff(3387,plain,
% 0.70/0.95 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.95 inference(transitivity,[status(thm)],[3386, 3384])).
% 0.70/0.95 tff(3388,plain,
% 0.70/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.70/0.95 inference(quant_inst,[status(thm)],[])).
% 0.70/0.95 tff(3389,plain,
% 0.70/0.95 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(elem!1))))) | (~b(s(elem!1), s(s(s(elem!1))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3388, 3387])).
% 0.70/0.95 tff(3390,plain,
% 0.70/0.95 ($false),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3389, 272, 3383, 3377, 2025])).
% 0.70/0.95 tff(3391,plain,((~r(z, s(s(s(z))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~(z = elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.95 tff(3392,plain,
% 0.70/0.95 (~r(z, s(s(s(z))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3391, 3359, 2394, 3354, 3353, 3342])).
% 0.70/0.95 tff(3393,plain,
% 0.70/0.95 (b(z, s(s(s(z))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[1541, 3392])).
% 0.70/0.95 tff(3394,plain,
% 0.70/0.95 (b(elem!1, s(s(s(elem!1))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3393, 3336])).
% 0.70/0.95 tff(3395,plain,
% 0.70/0.95 (~b(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3198, 3394, 3328])).
% 0.70/0.95 tff(3396,plain,
% 0.70/0.95 (r(s(s(z)), s(s(s(z)))) <=> r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3330, 3331])).
% 0.70/0.95 tff(3397,plain,
% 0.70/0.95 (b(s(s(z)), z) <=> b(s(s(z)), elem!1)),
% 0.70/0.95 inference(monotonicity,[status(thm)],[2394])).
% 0.70/0.95 tff(3398,plain,
% 0.70/0.95 (b(s(s(z)), elem!1) <=> b(s(s(z)), z)),
% 0.70/0.95 inference(symmetry,[status(thm)],[3397])).
% 0.70/0.95 tff(3399,plain,
% 0.70/0.95 (b(s(s(z)), elem!1) <=> b(s(s(elem!1)), elem!1)),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3330])).
% 0.70/0.95 tff(3400,plain,
% 0.70/0.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), elem!1)),
% 0.70/0.95 inference(symmetry,[status(thm)],[3399])).
% 0.70/0.95 tff(3401,plain,
% 0.70/0.95 (b(s(s(elem!1)), elem!1) <=> b(s(s(z)), z)),
% 0.70/0.95 inference(transitivity,[status(thm)],[3400, 3398])).
% 0.70/0.95 tff(3402,plain,
% 0.70/0.95 (b(s(s(z)), z)),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3224, 3401])).
% 0.70/0.95 tff(3403,plain,
% 0.70/0.95 (~b(s(s(z)), s(s(s(z))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3274, 3393, 3402])).
% 0.70/0.95 tff(3404,plain,
% 0.70/0.95 (r(s(s(z)), s(s(s(z))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3288, 3403])).
% 0.70/0.95 tff(3405,plain,
% 0.70/0.95 (r(s(s(elem!1)), s(s(s(elem!1))))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[3404, 3396])).
% 0.70/0.95 tff(3406,plain,
% 0.70/0.95 (~r(s(s(s(s(s(s(elem!1)))))), s(s(s(elem!1))))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3138, 3405, 3351])).
% 0.70/0.95 tff(3407,plain,
% 0.70/0.95 ($false),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2524, 3406, 3395, 2384])).
% 0.70/0.95 tff(3408,plain,((s(s(s(s(s(s(elem!1)))))) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.95 tff(3409,plain,
% 0.70/0.95 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[3408, 248])).
% 0.70/0.95 tff(3410,plain,
% 0.70/0.95 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = z)),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3409])).
% 0.70/0.95 tff(3411,plain,
% 0.70/0.95 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (z = elem!1)),
% 0.70/0.95 inference(transitivity,[status(thm)],[3410, 2])).
% 0.70/0.95 tff(3412,plain,
% 0.70/0.95 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(z = elem!1))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3411])).
% 0.70/0.95 tff(3413,plain,
% 0.70/0.95 (~(z = elem!1)),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[558, 3412])).
% 0.70/0.95 tff(3414,plain,
% 0.70/0.95 (~(s(elem!1) = s(s(elem!1)))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[623, 3010])).
% 0.70/0.95 tff(3415,plain,
% 0.70/0.95 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3409])).
% 0.70/0.95 tff(3416,plain,
% 0.70/0.95 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.95 inference(symmetry,[status(thm)],[3415])).
% 0.70/0.95 tff(3417,plain,
% 0.70/0.95 ((s(elem!1) = s(z)) <=> (s(s(s(s(s(s(s(elem!1))))))) = s(z))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3416])).
% 0.70/0.95 tff(3418,plain,
% 0.70/0.95 ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) <=> (s(elem!1) = s(z))),
% 0.70/0.95 inference(symmetry,[status(thm)],[3417])).
% 0.70/0.95 tff(3419,plain,
% 0.70/0.95 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(z))) <=> (~(s(elem!1) = s(z)))),
% 0.70/0.95 inference(monotonicity,[status(thm)],[3418])).
% 0.70/0.95 tff(3420,plain,
% 0.70/0.95 (~(s(elem!1) = s(z))),
% 0.70/0.95 inference(modus_ponens,[status(thm)],[1643, 3419])).
% 0.70/0.95 tff(3421,plain,
% 0.70/0.95 (~(s(elem!1) = elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[246, 3010])).
% 0.70/0.95 tff(3422,plain,
% 0.70/0.95 (~(s(s(z)) = elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[219, 3409])).
% 0.70/0.95 tff(3423,plain,
% 0.70/0.95 (b(s(z), elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[143, 128, 252])).
% 0.70/0.95 tff(3424,plain,
% 0.70/0.95 (~b(s(z), s(s(elem!1)))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[850, 272, 3423, 864])).
% 0.70/0.95 tff(3425,plain,
% 0.70/0.95 (r(s(z), s(s(elem!1)))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[862, 3424])).
% 0.70/0.95 tff(3426,plain,
% 0.70/0.95 (~b(s(s(elem!1)), s(z))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[878, 272, 3423, 864])).
% 0.70/0.95 tff(3427,plain,
% 0.70/0.95 (r(s(s(elem!1)), s(z))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[890, 3426])).
% 0.70/0.95 tff(3428,plain,
% 0.70/0.95 (~(s(s(z)) = s(s(elem!1)))),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[2391, 3420])).
% 0.70/0.95 tff(3429,plain,
% 0.70/0.95 (~b(s(s(z)), elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[896, 3423, 3428, 864])).
% 0.70/0.95 tff(3430,plain,
% 0.70/0.95 (r(s(s(z)), elem!1)),
% 0.70/0.95 inference(unit_resolution,[status(thm)],[476, 3429, 3422])).
% 0.70/0.95 tff(3431,plain,
% 0.70/0.95 ((s(s(s(s(s(s(elem!1)))))) = z) <=> (elem!1 = z)),
% 0.70/0.95 inference(transitivity,[status(thm)],[3411, 3])).
% 0.70/0.95 tff(3432,plain,
% 0.70/0.95 ((~(s(s(s(s(s(s(elem!1)))))) = z)) <=> (~(elem!1 = z))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3431])).
% 0.70/0.96 tff(3433,plain,
% 0.70/0.96 (~(elem!1 = z)),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[558, 3432])).
% 0.70/0.96 tff(3434,assumption,(~b(s(z), s(s(elem!1)))), introduced(assumption)).
% 0.70/0.96 tff(3435,plain,
% 0.70/0.96 (r(s(z), s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[862, 3434])).
% 0.70/0.96 tff(3436,plain,
% 0.70/0.96 ((s(s(z)) = s(s(elem!1))) <=> (s(s(elem!1)) = s(s(z)))),
% 0.70/0.96 inference(symmetry,[status(thm)],[743])).
% 0.70/0.96 tff(3437,plain,
% 0.70/0.96 ((~(s(s(z)) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(z))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3436])).
% 0.70/0.96 tff(3438,plain,
% 0.70/0.96 (~(s(s(elem!1)) = s(s(z)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3428, 3437])).
% 0.70/0.96 tff(3439,assumption,(b(s(elem!1), s(s(z)))), introduced(assumption)).
% 0.70/0.96 tff(3440,assumption,(b(s(s(z)), s(z))), introduced(assumption)).
% 0.70/0.96 tff(3441,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1119, 272, 308, 3440, 3439])).
% 0.70/0.96 tff(3442,plain,((~b(s(s(z)), s(z))) | (~b(s(elem!1), s(z))) | (~b(s(elem!1), s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3443,plain,
% 0.70/0.96 (~b(s(s(z)), s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3442, 308, 642])).
% 0.70/0.96 tff(3444,plain,
% 0.70/0.96 (r(s(s(z)), s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[359, 3443])).
% 0.70/0.96 tff(3445,plain,
% 0.70/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3446,plain,
% 0.70/0.96 (((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3447,plain,
% 0.70/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3446])).
% 0.70/0.96 tff(3448,plain,
% 0.70/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z))))),
% 0.70/0.96 inference(transitivity,[status(thm)],[3447, 3445])).
% 0.70/0.96 tff(3449,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(z))) | (~r(s(s(elem!1)), s(s(z)))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3450,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(elem!1)), s(s(z)))) | (~r(s(s(elem!1)), s(z)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3449, 3448])).
% 0.70/0.96 tff(3451,plain,
% 0.70/0.96 (~r(s(s(elem!1)), s(s(z)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3450, 371, 943, 3444])).
% 0.70/0.96 tff(3452,plain,
% 0.70/0.96 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3453,plain,
% 0.70/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3454,plain,
% 0.70/0.96 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z))) | r(s(s(elem!1)), s(s(z)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3453, 3452])).
% 0.70/0.96 tff(3455,plain,
% 0.70/0.96 ((s(s(elem!1)) = s(s(z))) | b(s(s(elem!1)), s(s(z)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3454, 139, 3451])).
% 0.70/0.96 tff(3456,plain,
% 0.70/0.96 (b(s(s(elem!1)), s(s(z)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3455, 3438])).
% 0.70/0.96 tff(3457,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3458,plain,
% 0.70/0.96 (((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1)))) <=> ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3459,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z)))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3458])).
% 0.70/0.96 tff(3460,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))))),
% 0.70/0.96 inference(transitivity,[status(thm)],[3459, 3457])).
% 0.70/0.96 tff(3461,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z))) | (~b(s(s(elem!1)), s(elem!1))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3462,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(z)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3461, 3460])).
% 0.70/0.96 tff(3463,plain,
% 0.70/0.96 (~b(s(s(elem!1)), s(elem!1))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3462, 272, 308, 642, 3456])).
% 0.70/0.96 tff(3464,plain,
% 0.70/0.96 (r(s(s(elem!1)), s(elem!1))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[660, 3463, 3010])).
% 0.70/0.96 tff(3465,plain,
% 0.70/0.96 (~(s(z) = s(elem!1))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[11, 294])).
% 0.70/0.96 tff(3466,plain,
% 0.70/0.96 (~r(s(z), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1027, 903, 1019])).
% 0.70/0.96 tff(3467,plain,
% 0.70/0.96 (b(s(z), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[287, 139, 284, 3466])).
% 0.70/0.96 tff(3468,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3469,plain,
% 0.70/0.96 (((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))) <=> ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3470,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3469])).
% 0.70/0.96 tff(3471,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 0.70/0.96 inference(transitivity,[status(thm)],[3470, 3468])).
% 0.70/0.96 tff(3472,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3473,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(elem!1), z)) | (~b(s(z), s(elem!1)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3472, 3471])).
% 0.70/0.96 tff(3474,plain,
% 0.70/0.96 (~b(s(z), s(elem!1))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3473, 272, 3467, 1561])).
% 0.70/0.96 tff(3475,plain,
% 0.70/0.96 ((s(z) = s(elem!1)) | r(s(z), s(elem!1))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[305, 139, 3474])).
% 0.70/0.96 tff(3476,plain,
% 0.70/0.96 (r(s(z), s(elem!1))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3475, 3465])).
% 0.70/0.96 tff(3477,plain,
% 0.70/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3478,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1)))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3479,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(z), s(elem!1))) | (~r(s(z), s(s(elem!1))))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3478, 3477])).
% 0.70/0.96 tff(3480,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3479, 371, 1215, 903, 3476])).
% 0.70/0.96 tff(3481,plain,((~r(s(z), s(s(elem!1)))) | (~r(s(s(elem!1)), s(elem!1))) | (s(elem!1) = s(z)) | (~r(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3482,plain,
% 0.70/0.96 (~r(s(s(elem!1)), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3481, 3464, 3420, 3435])).
% 0.70/0.96 tff(3483,plain,
% 0.70/0.96 (b(s(s(elem!1)), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[453, 3482])).
% 0.70/0.96 tff(3484,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3485,plain,
% 0.70/0.96 (((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3486,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3485])).
% 0.70/0.96 tff(3487,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z)))))),
% 0.70/0.96 inference(transitivity,[status(thm)],[3486, 3484])).
% 0.70/0.96 tff(3488,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(s(elem!1)), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3489,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(z)))) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), s(s(z))))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3488, 3487])).
% 0.70/0.96 tff(3490,plain,
% 0.70/0.96 (~b(s(elem!1), s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3489, 272, 642, 3456])).
% 0.70/0.96 tff(3491,plain,
% 0.70/0.96 (r(s(elem!1), s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[635, 3490, 3414])).
% 0.70/0.96 tff(3492,plain,
% 0.70/0.96 (~r(elem!1, s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1052, 3491, 637])).
% 0.70/0.96 tff(3493,plain,
% 0.70/0.96 (b(elem!1, s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1045, 3492, 96])).
% 0.70/0.96 tff(3494,plain,
% 0.70/0.96 (~b(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1040, 3493, 3483])).
% 0.70/0.96 tff(3495,plain,
% 0.70/0.96 (r(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[997, 3494, 3433])).
% 0.70/0.96 tff(3496,plain,
% 0.70/0.96 (b(elem!1, s(s(elem!1))) <=> b(s(z), s(s(elem!1)))),
% 0.70/0.96 inference(symmetry,[status(thm)],[2108])).
% 0.70/0.96 tff(3497,plain,
% 0.70/0.96 (b(s(z), s(s(elem!1)))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[1031, 3496])).
% 0.70/0.96 tff(3498,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3434, 3497])).
% 0.70/0.96 tff(3499,plain,((~(s(z) = elem!1)) | b(s(z), s(s(elem!1))) | (~b(elem!1, s(s(elem!1))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3500,plain,
% 0.70/0.96 (~(s(z) = elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3499, 1031, 3434])).
% 0.70/0.96 tff(3501,plain,
% 0.70/0.96 (b(s(z), elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[143, 3500, 128])).
% 0.70/0.96 tff(3502,plain,
% 0.70/0.96 (~b(s(elem!1), elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[316, 3501, 308])).
% 0.70/0.96 tff(3503,plain,
% 0.70/0.96 (r(s(elem!1), elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[618, 3502, 1556])).
% 0.70/0.96 tff(3504,plain,
% 0.70/0.96 (~b(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1040, 1031, 1030])).
% 0.70/0.96 tff(3505,plain,
% 0.70/0.96 (r(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[997, 3504, 5])).
% 0.70/0.96 tff(3506,plain,
% 0.70/0.96 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3507,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1)))),
% 0.70/0.96 inference(quant_inst,[status(thm)],[])).
% 0.70/0.96 tff(3508,plain,
% 0.70/0.96 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(elem!1), z)) | (~r(s(elem!1), elem!1))),
% 0.70/0.96 inference(modus_ponens,[status(thm)],[3507, 3506])).
% 0.70/0.96 tff(3509,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3508, 371, 3505, 416, 3503])).
% 0.70/0.96 tff(3510,plain,((~b(elem!1, s(s(elem!1)))) | (~r(s(elem!1), z)) | (s(elem!1) = elem!1) | (~b(s(elem!1), s(z))) | r(s(z), elem!1) | (elem!1 = z) | b(s(z), s(s(elem!1))) | (~b(s(s(elem!1)), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3511,plain,
% 0.70/0.96 (~r(s(elem!1), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3510, 3483, 3433, 3421, 128, 3493, 308, 3434])).
% 0.70/0.96 tff(3512,plain,
% 0.70/0.96 (b(s(elem!1), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[414, 3511])).
% 0.70/0.96 tff(3513,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[992, 3512, 3495, 248, 637, 434])).
% 0.70/0.96 tff(3514,plain,((~b(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), elem!1)) | (~r(s(s(z)), elem!1)) | r(s(z), elem!1) | b(s(z), s(s(elem!1))) | (elem!1 = s(s(elem!1))) | (~r(s(s(elem!1)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3515,plain,
% 0.70/0.96 (~b(s(elem!1), s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3514, 3430, 637, 248, 128, 3424, 96, 3427])).
% 0.70/0.96 tff(3516,plain,
% 0.70/0.96 (r(s(elem!1), s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[324, 3515, 3420])).
% 0.70/0.96 tff(3517,plain,
% 0.70/0.96 (~r(s(elem!1), s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[911, 3516, 3425])).
% 0.70/0.96 tff(3518,plain,
% 0.70/0.96 (b(s(elem!1), s(s(elem!1)))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[635, 3517, 3414])).
% 0.70/0.96 tff(3519,plain,
% 0.70/0.96 (~r(z, s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[425, 416, 361])).
% 0.70/0.96 tff(3520,plain,
% 0.70/0.96 (b(z, s(z))),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[397, 3519])).
% 0.70/0.96 tff(3521,plain,
% 0.70/0.96 (~r(z, elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[828, 416, 637])).
% 0.70/0.96 tff(3522,plain,
% 0.70/0.96 (b(z, elem!1)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[432, 3521, 1362])).
% 0.70/0.96 tff(3523,plain,
% 0.70/0.96 ($false),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[387, 3522, 3520, 253])).
% 0.70/0.96 tff(3524,plain,((~r(s(elem!1), z)) | (~b(s(z), elem!1)) | (z = elem!1) | (~r(s(elem!1), elem!1)) | (~r(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.96 tff(3525,plain,
% 0.70/0.96 (~r(s(elem!1), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[3524, 3516, 3423, 3413, 637])).
% 0.70/0.96 tff(3526,plain,
% 0.70/0.96 (b(s(elem!1), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[414, 3525])).
% 0.70/0.96 tff(3527,plain,
% 0.70/0.96 (~r(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[992, 3526, 248, 637, 3430])).
% 0.70/0.96 tff(3528,plain,
% 0.70/0.96 (b(elem!1, z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[997, 3527, 3433])).
% 0.70/0.96 tff(3529,plain,
% 0.70/0.96 (~b(s(z), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1005, 3528, 3423])).
% 0.70/0.96 tff(3530,plain,
% 0.70/0.96 (r(s(z), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[289, 3529])).
% 0.70/0.96 tff(3531,plain,
% 0.70/0.96 (~r(s(s(elem!1)), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[1027, 3530, 3425])).
% 0.70/0.96 tff(3532,plain,
% 0.70/0.96 (b(s(s(elem!1)), z)),
% 0.70/0.96 inference(unit_resolution,[status(thm)],[453, 3531])).
% 0.70/0.96 tff(3533,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3534,plain,
% 0.70/0.96 (((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1))))) <=> ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.70/0.96 inference(rewrite,[status(thm)],[])).
% 0.70/0.96 tff(3535,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))))),
% 0.70/0.96 inference(monotonicity,[status(thm)],[3534])).
% 0.70/0.96 tff(3536,plain,
% 0.70/0.96 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z)))),
% 0.70/0.96 inference(transitivity,[status(thm)],[3535, 3533])).
% 0.70/0.96 tff(3537,plain,
% 0.70/0.96 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(elem!1), z)) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), s(s(elem!1)))))),
% 0.70/0.97 inference(quant_inst,[status(thm)],[])).
% 0.70/0.97 tff(3538,plain,
% 0.70/0.97 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(s(elem!1)))) | (~b(s(s(elem!1)), z))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3537, 3536])).
% 0.70/0.97 tff(3539,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3538, 272, 3526, 864, 3532, 3518])).
% 0.70/0.97 tff(3540,plain,(r(s(z), elem!1) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(z))) | (~r(s(elem!1), elem!1)) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3541,plain,
% 0.70/0.97 (r(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3540, 637, 248, 864, 96])).
% 0.70/0.97 tff(3542,plain,
% 0.70/0.97 (~r(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1106, 3541, 637])).
% 0.70/0.97 tff(3543,plain,
% 0.70/0.97 (b(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[324, 3542, 3420])).
% 0.70/0.97 tff(3544,plain,
% 0.70/0.97 (~r(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1121, 3543, 248, 637, 3541])).
% 0.70/0.97 tff(3545,plain,
% 0.70/0.97 (~r(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1318, 3541, 3420, 637])).
% 0.70/0.97 tff(3546,plain,
% 0.70/0.97 (b(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[432, 3545, 3413])).
% 0.70/0.97 tff(3547,plain,
% 0.70/0.97 (~b(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1139, 3546, 3428, 864])).
% 0.70/0.97 tff(3548,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[476, 3547, 3544, 3422])).
% 0.70/0.97 tff(3549,plain,((~r(s(elem!1), elem!1)) | (~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(z))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3550,plain,
% 0.70/0.97 (~r(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3549, 864, 248, 96])).
% 0.70/0.97 tff(3551,plain,
% 0.70/0.97 (b(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[618, 3550, 3421])).
% 0.70/0.97 tff(3552,plain,
% 0.70/0.97 (~b(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[921, 3551, 3420, 3414, 864])).
% 0.70/0.97 tff(3553,plain,
% 0.70/0.97 (~r(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1381, 3551, 3422, 3413, 864, 248, 3428, 3010])).
% 0.70/0.97 tff(3554,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[143, 3553, 3552, 252])).
% 0.70/0.97 tff(3555,plain,((~b(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(z))) | (elem!1 = s(s(elem!1)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3556,plain,
% 0.70/0.97 (~b(s(s(elem!1)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3555, 2371, 248])).
% 0.70/0.97 tff(3557,plain,
% 0.70/0.97 (r(s(s(elem!1)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[843, 3556, 233])).
% 0.70/0.97 tff(3558,plain,
% 0.70/0.97 (~(s(elem!1) = s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[623, 2372])).
% 0.70/0.97 tff(3559,plain,
% 0.70/0.97 (r(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[324, 317, 3420])).
% 0.70/0.97 tff(3560,plain,
% 0.70/0.97 (~b(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[379, 3559, 248, 253, 291])).
% 0.70/0.97 tff(3561,plain,
% 0.70/0.97 (r(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[476, 3560, 3422])).
% 0.70/0.97 tff(3562,plain,
% 0.70/0.97 (~b(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[427, 3559, 253, 291])).
% 0.70/0.97 tff(3563,plain,
% 0.70/0.97 (r(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[432, 3562, 3413])).
% 0.70/0.97 tff(3564,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[471, 3563, 3561, 254, 3428])).
% 0.70/0.97 tff(3565,plain,((~b(s(elem!1), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (~b(s(z), elem!1)) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3566,plain,
% 0.70/0.97 (~b(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3565, 253, 254, 248])).
% 0.70/0.97 tff(3567,plain,
% 0.70/0.97 (r(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[618, 3566, 1556])).
% 0.70/0.97 tff(3568,plain,
% 0.70/0.97 (~r(s(elem!1), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[630, 371, 254, 3567])).
% 0.70/0.97 tff(3569,plain,
% 0.70/0.97 (b(s(elem!1), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[635, 3568, 898])).
% 0.70/0.97 tff(3570,plain,
% 0.70/0.97 (~r(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[651, 3569, 248, 3428, 254, 3567])).
% 0.70/0.97 tff(3571,plain,
% 0.70/0.97 (b(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[476, 3570, 3422])).
% 0.70/0.97 tff(3572,plain,
% 0.70/0.97 (~b(s(s(z)), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[787, 262, 326])).
% 0.70/0.97 tff(3573,plain,
% 0.70/0.97 (r(s(s(z)), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[462, 3572])).
% 0.70/0.97 tff(3574,plain,
% 0.70/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.70/0.97 inference(rewrite,[status(thm)],[])).
% 0.70/0.97 tff(3575,plain,
% 0.70/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z))))),
% 0.70/0.97 inference(quant_inst,[status(thm)],[])).
% 0.70/0.97 tff(3576,plain,
% 0.70/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(z)))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3575, 3574])).
% 0.70/0.97 tff(3577,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3576, 371, 3573, 290, 360])).
% 0.70/0.97 tff(3578,plain,((~b(z, elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3579,plain,
% 0.70/0.97 (~b(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3578, 253, 3571])).
% 0.70/0.97 tff(3580,plain,
% 0.70/0.97 (r(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[432, 3579, 3413])).
% 0.70/0.97 tff(3581,plain,
% 0.70/0.97 (~r(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[828, 3580, 3567])).
% 0.70/0.97 tff(3582,plain,
% 0.70/0.97 (b(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[414, 3581])).
% 0.70/0.97 tff(3583,plain,
% 0.70/0.97 (~b(z, s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1546, 3582, 3569])).
% 0.70/0.97 tff(3584,plain,
% 0.70/0.97 (r(z, s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[579, 3583])).
% 0.70/0.97 tff(3585,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[569, 371, 3580, 254, 3584])).
% 0.70/0.97 tff(3586,plain,((~b(s(z), elem!1)) | (~r(s(s(elem!1)), elem!1)) | (s(elem!1) = s(s(z))) | (s(elem!1) = s(s(elem!1))) | (s(elem!1) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3587,plain,
% 0.70/0.97 (~b(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3586, 3557, 248, 3558, 2373])).
% 0.70/0.97 tff(3588,plain,
% 0.70/0.97 (r(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[143, 3587, 252])).
% 0.70/0.97 tff(3589,plain,
% 0.70/0.97 (~r(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1343, 3588, 3557])).
% 0.70/0.97 tff(3590,plain,
% 0.70/0.97 (b(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[432, 3589, 3413])).
% 0.70/0.97 tff(3591,plain,
% 0.70/0.97 (~b(s(s(z)), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1294, 272, 1332, 1113])).
% 0.70/0.97 tff(3592,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[441, 139, 203, 3591, 438])).
% 0.70/0.97 tff(3593,plain,((~r(s(s(z)), elem!1)) | (s(s(z)) = s(s(elem!1))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3594,plain,
% 0.70/0.97 (~r(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3593, 3557, 3428, 3588])).
% 0.70/0.97 tff(3595,plain,
% 0.70/0.97 (b(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[476, 3594, 3422])).
% 0.70/0.97 tff(3596,plain,
% 0.70/0.97 (~b(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1213, 3595, 248, 3590])).
% 0.70/0.97 tff(3597,plain,
% 0.70/0.97 (r(s(elem!1), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[618, 3596, 2373])).
% 0.70/0.97 tff(3598,plain,
% 0.70/0.97 (~r(s(s(elem!1)), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1188, 371, 3588, 3557])).
% 0.70/0.97 tff(3599,plain,
% 0.70/0.97 (b(s(s(elem!1)), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[890, 3598])).
% 0.70/0.97 tff(3600,plain,
% 0.70/0.97 (~r(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1106, 3597, 3588])).
% 0.70/0.97 tff(3601,plain,
% 0.70/0.97 (b(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[324, 3600, 3420])).
% 0.70/0.97 tff(3602,plain,
% 0.70/0.97 (~b(s(s(elem!1)), s(elem!1))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1201, 3601, 3599])).
% 0.70/0.97 tff(3603,plain,
% 0.70/0.97 (r(s(s(elem!1)), s(elem!1))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[660, 3602, 2372])).
% 0.70/0.97 tff(3604,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[655, 371, 3603, 3557, 3597])).
% 0.70/0.97 tff(3605,plain,((s(s(elem!1)) = elem!1) | (s(elem!1) = s(s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3606,plain,
% 0.70/0.97 (s(s(elem!1)) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3605, 2370])).
% 0.70/0.97 tff(3607,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3408, 2370])).
% 0.70/0.97 tff(3608,plain,
% 0.70/0.97 ((~![Xk!0: $i] : (inj_0(s(Xk!0)) = Xk!0)) | (inj_0(s(s(s(s(z))))) = s(s(s(z))))),
% 0.70/0.97 inference(quant_inst,[status(thm)],[])).
% 0.70/0.97 tff(3609,plain,
% 0.70/0.97 (inj_0(s(s(s(s(z))))) = s(s(s(z)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3608, 22])).
% 0.70/0.97 tff(3610,assumption,(s(s(s(s(z)))) = elem!1), introduced(assumption)).
% 0.70/0.97 tff(3611,plain,
% 0.70/0.97 (s(s(s(s(z)))) = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3610, 208])).
% 0.70/0.97 tff(3612,plain,
% 0.70/0.97 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3611])).
% 0.70/0.97 tff(3613,plain,
% 0.70/0.97 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(s(s(z)))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3612])).
% 0.70/0.97 tff(3614,plain,
% 0.70/0.97 (elem!1 = s(s(elem!1))),
% 0.70/0.97 inference(symmetry,[status(thm)],[222])).
% 0.70/0.97 tff(3615,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))),
% 0.70/0.97 inference(transitivity,[status(thm)],[207, 3614])).
% 0.70/0.97 tff(3616,plain,
% 0.70/0.97 (inj_0(s(s(s(s(s(s(elem!1))))))) = inj_0(s(s(elem!1)))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3615])).
% 0.70/0.97 tff(3617,plain,
% 0.70/0.97 (inj_0(s(s(elem!1))) = inj_0(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3616])).
% 0.70/0.97 tff(3618,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[208])).
% 0.70/0.97 tff(3619,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/0.97 inference(symmetry,[status(thm)],[3618])).
% 0.70/0.97 tff(3620,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(elem!1)))),
% 0.70/0.97 inference(symmetry,[status(thm)],[223])).
% 0.70/0.97 tff(3621,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[207])).
% 0.70/0.97 tff(3622,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3621, 3620])).
% 0.70/0.97 tff(3623,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2510, 3622])).
% 0.70/0.97 tff(3624,plain,((~(s(s(elem!1)) = elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3625,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3624, 207, 222])).
% 0.70/0.97 tff(3626,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3625])).
% 0.70/0.97 tff(3627,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(s(s(z)))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3626, 3619, 68, 3617, 3613, 3609])).
% 0.70/0.97 tff(3628,plain,
% 0.70/0.97 (~(s(s(z)) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[219, 207])).
% 0.70/0.97 tff(3629,assumption,(s(s(s(elem!1))) = s(s(s(z)))), introduced(assumption)).
% 0.70/0.97 tff(3630,plain,
% 0.70/0.97 (s(s(s(z))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3629])).
% 0.70/0.97 tff(3631,plain,
% 0.70/0.97 (inj_0(s(s(s(z)))) = inj_0(s(s(s(elem!1))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3630])).
% 0.70/0.97 tff(3632,plain,
% 0.70/0.97 (s(s(z)) = elem!1),
% 0.70/0.97 inference(transitivity,[status(thm)],[191, 3631, 601, 222])).
% 0.70/0.97 tff(3633,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1346, 3632])).
% 0.70/0.97 tff(3634,plain,((~(s(s(s(elem!1))) = s(s(s(z))))) | (s(s(z)) = elem!1) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3635,plain,
% 0.70/0.97 (~(s(s(s(elem!1))) = s(s(s(z))))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3634, 3628, 222])).
% 0.70/0.97 tff(3636,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3635, 3627])).
% 0.70/0.97 tff(3637,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3638,plain,
% 0.70/0.97 (~(s(s(s(s(z)))) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3637, 3607, 3606])).
% 0.70/0.97 tff(3639,plain,
% 0.70/0.97 (~(s(s(z)) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[219, 3607])).
% 0.70/0.97 tff(3640,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3624, 3606, 3607])).
% 0.70/0.97 tff(3641,plain,
% 0.70/0.97 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2232, 3640])).
% 0.70/0.97 tff(3642,plain,
% 0.70/0.97 (~(s(elem!1) = s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[50, 3641])).
% 0.70/0.97 tff(3643,plain,
% 0.70/0.97 (~(s(elem!1) = s(s(z)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1418, 1416])).
% 0.70/0.97 tff(3644,plain,
% 0.70/0.97 (s(s(elem!1)) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3605, 3643])).
% 0.70/0.97 tff(3645,assumption,(elem!1 = s(s(s(z)))), introduced(assumption)).
% 0.70/0.97 tff(3646,plain,
% 0.70/0.97 (s(s(s(z))) = elem!1),
% 0.70/0.97 inference(symmetry,[status(thm)],[3645])).
% 0.70/0.97 tff(3647,plain,
% 0.70/0.97 (s(s(s(z))) = s(s(elem!1))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3646, 3614])).
% 0.70/0.97 tff(3648,plain,
% 0.70/0.97 (inj_0(s(s(s(z)))) = inj_0(s(s(elem!1)))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3647])).
% 0.70/0.97 tff(3649,plain,
% 0.70/0.97 (inj_0(s(s(elem!1))) = inj_0(s(s(s(z))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3648])).
% 0.70/0.97 tff(3650,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(elem!1)))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3614])).
% 0.70/0.97 tff(3651,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(elem!1)),
% 0.70/0.97 inference(symmetry,[status(thm)],[3650])).
% 0.70/0.97 tff(3652,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(s(z))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3651, 68, 3649, 190])).
% 0.70/0.97 tff(3653,plain,
% 0.70/0.97 ((s(elem!1) = s(s(z))) <=> (s(s(s(elem!1))) = s(s(z)))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3650])).
% 0.70/0.97 tff(3654,plain,
% 0.70/0.97 ((~(s(elem!1) = s(s(z)))) <=> (~(s(s(s(elem!1))) = s(s(z))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3653])).
% 0.70/0.97 tff(3655,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[230, 222])).
% 0.70/0.97 tff(3656,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3624, 3655, 222])).
% 0.70/0.97 tff(3657,plain,
% 0.70/0.97 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2232, 3656])).
% 0.70/0.97 tff(3658,plain,
% 0.70/0.97 (~(s(z) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[172, 3657])).
% 0.70/0.97 tff(3659,plain,
% 0.70/0.97 (~(s(elem!1) = s(s(z)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1418, 3658])).
% 0.70/0.97 tff(3660,plain,
% 0.70/0.97 (~(s(s(s(elem!1))) = s(s(z)))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3659, 3654])).
% 0.70/0.97 tff(3661,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3660, 3652])).
% 0.70/0.97 tff(3662,plain,((~(elem!1 = s(s(s(z))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3663,plain,
% 0.70/0.97 (~(elem!1 = s(s(s(z))))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3662, 3644])).
% 0.70/0.97 tff(3664,plain,
% 0.70/0.97 ((s(s(s(z))) = elem!1) <=> (elem!1 = s(s(s(z))))),
% 0.70/0.97 inference(commutativity,[status(thm)],[])).
% 0.70/0.97 tff(3665,assumption,(s(s(s(z))) = elem!1), introduced(assumption)).
% 0.70/0.97 tff(3666,plain,
% 0.70/0.97 (elem!1 = s(s(s(z)))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3665, 3664])).
% 0.70/0.97 tff(3667,assumption,(~(elem!1 = s(s(s(z))))), introduced(assumption)).
% 0.70/0.97 tff(3668,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3667, 3666])).
% 0.70/0.97 tff(3669,plain,((~(s(s(s(z))) = elem!1)) | (elem!1 = s(s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3670,plain,
% 0.70/0.97 (~(s(s(s(z))) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3669, 3663])).
% 0.70/0.97 tff(3671,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3408, 3643])).
% 0.70/0.97 tff(3672,plain,
% 0.70/0.97 (~(s(s(z)) = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[219, 3671])).
% 0.70/0.97 tff(3673,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3624, 3671, 3644])).
% 0.70/0.97 tff(3674,plain,
% 0.70/0.97 (elem!1 = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3671])).
% 0.70/0.97 tff(3675,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3674])).
% 0.70/0.97 tff(3676,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(elem!1)))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3675, 3673])).
% 0.70/0.97 tff(3677,plain,
% 0.70/0.97 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3676])).
% 0.70/0.97 tff(3678,plain,
% 0.70/0.97 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2232, 3673])).
% 0.70/0.97 tff(3679,plain,
% 0.70/0.97 (~(s(elem!1) = s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[50, 3678])).
% 0.70/0.97 tff(3680,plain,
% 0.70/0.97 (~(elem!1 = z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[13, 3679])).
% 0.70/0.97 tff(3681,plain,
% 0.70/0.97 (~(z = elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[7, 3680])).
% 0.70/0.97 tff(3682,plain,
% 0.70/0.97 (b(z, elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[432, 3681, 1936])).
% 0.70/0.97 tff(3683,plain,
% 0.70/0.97 (r(elem!1, z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[997, 1867, 3680])).
% 0.70/0.97 tff(3684,plain,
% 0.70/0.97 (r(s(elem!1), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3676])).
% 0.70/0.97 tff(3685,plain,
% 0.70/0.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(elem!1), elem!1)),
% 0.70/0.97 inference(symmetry,[status(thm)],[3684])).
% 0.70/0.97 tff(3686,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3673])).
% 0.70/0.97 tff(3687,plain,
% 0.70/0.97 (r(s(s(s(elem!1))), elem!1) <=> r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3686])).
% 0.70/0.97 tff(3688,plain,
% 0.70/0.97 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1) <=> r(s(s(s(elem!1))), elem!1)),
% 0.70/0.97 inference(symmetry,[status(thm)],[3687])).
% 0.70/0.97 tff(3689,plain,
% 0.70/0.97 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1) <=> r(s(elem!1), elem!1)),
% 0.70/0.97 inference(transitivity,[status(thm)],[3688, 3685])).
% 0.70/0.97 tff(3690,plain,
% 0.70/0.97 (b(s(s(s(elem!1))), elem!1) <=> b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3686])).
% 0.70/0.97 tff(3691,plain,
% 0.70/0.97 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3676])).
% 0.70/0.97 tff(3692,plain,
% 0.70/0.97 (b(s(elem!1), elem!1) <=> b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.97 inference(transitivity,[status(thm)],[3691, 3690])).
% 0.70/0.97 tff(3693,plain,
% 0.70/0.97 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3692])).
% 0.70/0.97 tff(3694,plain,
% 0.70/0.97 (~b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[52, 3693])).
% 0.70/0.97 tff(3695,plain,
% 0.70/0.97 (r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1690, 1652, 3694])).
% 0.70/0.97 tff(3696,plain,
% 0.70/0.97 (r(s(elem!1), elem!1)),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3695, 3689])).
% 0.70/0.97 tff(3697,plain,
% 0.70/0.97 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3626])).
% 0.70/0.97 tff(3698,plain,
% 0.70/0.97 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.70/0.97 inference(transitivity,[status(thm)],[3697, 2181])).
% 0.70/0.97 tff(3699,plain,
% 0.70/0.97 (s(elem!1) = s(s(s(elem!1)))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3618, 3625])).
% 0.70/0.97 tff(3700,plain,
% 0.70/0.97 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3699])).
% 0.70/0.97 tff(3701,plain,
% 0.70/0.97 ((s(s(elem!1)) = s(elem!1)) <=> (elem!1 = s(elem!1))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[222])).
% 0.70/0.97 tff(3702,plain,
% 0.70/0.97 ((s(s(elem!1)) = s(elem!1)) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.70/0.97 inference(transitivity,[status(thm)],[3701, 3700, 3698])).
% 0.70/0.97 tff(3703,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[80, 3702])).
% 0.70/0.97 tff(3704,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1652, 3703])).
% 0.70/0.97 tff(3705,plain,((~(s(s(elem!1)) = s(elem!1))) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1)) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3706,plain,
% 0.70/0.97 (~(s(s(elem!1)) = s(elem!1))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3705, 1652, 3671, 3644])).
% 0.70/0.97 tff(3707,plain,
% 0.70/0.97 (~(s(elem!1) = s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[623, 3706])).
% 0.70/0.97 tff(3708,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1908, 371, 972, 1101, 672])).
% 0.70/0.97 tff(3709,plain,((~r(elem!1, z)) | (~r(s(z), elem!1)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3710,plain,
% 0.70/0.97 (~r(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3709, 672, 972])).
% 0.70/0.97 tff(3711,plain,
% 0.70/0.97 (b(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[143, 3710, 1416])).
% 0.70/0.97 tff(3712,plain,
% 0.70/0.97 (~b(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3578, 3711, 262])).
% 0.70/0.97 tff(3713,plain,
% 0.70/0.97 (r(s(s(z)), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[476, 3712, 3672])).
% 0.70/0.97 tff(3714,plain,
% 0.70/0.97 (~b(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[992, 3713, 3643, 972, 637])).
% 0.70/0.97 tff(3715,plain,
% 0.70/0.97 (r(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[414, 3714])).
% 0.70/0.97 tff(3716,plain,
% 0.70/0.97 (~r(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3524, 3715, 637, 3681, 3711])).
% 0.70/0.97 tff(3717,plain,
% 0.70/0.97 (r(s(s(elem!1)), z) <=> r(elem!1, z)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3644])).
% 0.70/0.97 tff(3718,plain,
% 0.70/0.97 (r(elem!1, z) <=> r(s(s(elem!1)), z)),
% 0.70/0.97 inference(symmetry,[status(thm)],[3717])).
% 0.70/0.97 tff(3719,plain,
% 0.70/0.97 (r(s(s(elem!1)), z)),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[972, 3718])).
% 0.70/0.97 tff(3720,plain,
% 0.70/0.97 (~r(s(elem!1), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2075, 371, 416, 1019])).
% 0.70/0.97 tff(3721,plain,
% 0.70/0.97 (b(s(elem!1), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[635, 3720, 898])).
% 0.70/0.97 tff(3722,plain,
% 0.70/0.97 (~r(s(z), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1027, 1019, 672])).
% 0.70/0.97 tff(3723,plain,
% 0.70/0.97 (b(s(z), s(s(elem!1)))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[862, 3722])).
% 0.70/0.97 tff(3724,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2085, 272, 3723, 3721, 308])).
% 0.70/0.97 tff(3725,plain,((~r(s(s(elem!1)), z)) | (~b(s(elem!1), s(z))) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), z)) | (~r(s(z), z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3726,plain,
% 0.70/0.97 (~b(s(elem!1), s(z))),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3725, 3715, 3719, 898, 672])).
% 0.70/0.97 tff(3727,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[324, 3726, 3716, 3679])).
% 0.70/0.97 tff(3728,plain,((~r(s(z), z)) | (s(elem!1) = s(s(elem!1))) | (~r(s(elem!1), elem!1)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3729,plain,
% 0.70/0.97 (~r(s(z), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3728, 3707, 3696, 3683, 3682, 1416])).
% 0.70/0.97 tff(3730,plain,
% 0.70/0.97 (b(s(z), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[289, 3729])).
% 0.70/0.97 tff(3731,plain,
% 0.70/0.97 (~b(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[279, 3730, 3682])).
% 0.70/0.97 tff(3732,plain,
% 0.70/0.97 (~b(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1967, 3731, 1936, 1867, 52])).
% 0.70/0.97 tff(3733,plain,
% 0.70/0.97 (r(s(elem!1), z)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[414, 3732])).
% 0.70/0.97 tff(3734,plain,
% 0.70/0.97 (r(s(s(s(elem!1))), z)),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3733, 3677])).
% 0.70/0.97 tff(3735,plain,
% 0.70/0.97 (r(s(s(s(elem!1))), elem!1)),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3695, 3688])).
% 0.70/0.97 tff(3736,plain,
% 0.70/0.97 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.70/0.97 inference(rewrite,[status(thm)],[])).
% 0.70/0.97 tff(3737,plain,
% 0.70/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.70/0.97 inference(quant_inst,[status(thm)],[])).
% 0.70/0.97 tff(3738,plain,
% 0.70/0.97 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(s(s(s(elem!1))), z)) | (~r(s(s(s(elem!1))), elem!1))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3737, 3736])).
% 0.70/0.97 tff(3739,plain,
% 0.70/0.97 ($false),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3738, 371, 3683, 3735, 3734])).
% 0.70/0.97 tff(3740,plain,((s(s(s(s(s(s(s(elem!1))))))) = elem!1) | r(z, elem!1) | b(elem!1, z) | b(s(elem!1), elem!1) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.97 tff(3741,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[3740, 1867, 1936, 52, 1416])).
% 0.70/0.97 tff(3742,plain,
% 0.70/0.97 (~b(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[279, 1308, 262])).
% 0.70/0.97 tff(3743,plain,
% 0.70/0.97 (r(s(z), elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[143, 3742, 1416])).
% 0.70/0.97 tff(3744,plain,
% 0.70/0.97 ((s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(elem!1))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3671])).
% 0.70/0.97 tff(3745,plain,
% 0.70/0.97 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3744])).
% 0.70/0.97 tff(3746,plain,
% 0.70/0.97 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(s(s(s(s(s(s(elem!1))))))))),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3686])).
% 0.70/0.97 tff(3747,plain,
% 0.70/0.97 ((elem!1 = s(s(s(elem!1)))) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.70/0.97 inference(transitivity,[status(thm)],[3746, 2181])).
% 0.70/0.97 tff(3748,plain,
% 0.70/0.97 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (elem!1 = s(s(s(elem!1))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3747])).
% 0.70/0.97 tff(3749,plain,
% 0.70/0.97 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))),
% 0.70/0.97 inference(transitivity,[status(thm)],[3748, 3745])).
% 0.70/0.97 tff(3750,assumption,(s(s(s(s(s(s(s(elem!1))))))) = elem!1), introduced(assumption)).
% 0.70/0.97 tff(3751,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1)))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3750, 3749])).
% 0.70/0.97 tff(3752,plain,
% 0.70/0.97 (s(s(s(elem!1))) = elem!1),
% 0.70/0.97 inference(transitivity,[status(thm)],[3686, 3750])).
% 0.70/0.97 tff(3753,plain,
% 0.70/0.97 (r(s(z), s(s(s(elem!1)))) <=> r(s(z), elem!1)),
% 0.70/0.97 inference(monotonicity,[status(thm)],[3752])).
% 0.70/0.97 tff(3754,plain,
% 0.70/0.97 (r(s(z), elem!1) <=> r(s(z), s(s(s(elem!1))))),
% 0.70/0.97 inference(symmetry,[status(thm)],[3753])).
% 0.70/0.97 tff(3755,plain,
% 0.70/0.97 (r(s(z), s(s(s(elem!1))))),
% 0.70/0.97 inference(modus_ponens,[status(thm)],[3743, 3754])).
% 0.70/0.97 tff(3756,plain,
% 0.70/0.97 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[2383, 2374])).
% 0.70/0.97 tff(3757,plain,
% 0.70/0.97 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.97 inference(unit_resolution,[status(thm)],[1657, 3756])).
% 0.70/0.97 tff(3758,plain,
% 0.70/0.97 (s(s(s(elem!1))) = s(s(s(s(s(s(elem!1))))))),
% 0.70/0.98 inference(symmetry,[status(thm)],[2374])).
% 0.70/0.98 tff(3759,plain,
% 0.70/0.98 (s(s(s(elem!1))) = elem!1),
% 0.70/0.98 inference(transitivity,[status(thm)],[3758, 3757])).
% 0.70/0.98 tff(3760,plain,
% 0.70/0.98 (r(s(s(z)), s(s(s(elem!1)))) <=> r(s(s(z)), elem!1)),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3759])).
% 0.70/0.98 tff(3761,plain,
% 0.70/0.98 (r(s(s(z)), elem!1) <=> r(s(s(z)), s(s(s(elem!1))))),
% 0.70/0.98 inference(symmetry,[status(thm)],[3760])).
% 0.70/0.98 tff(3762,plain,
% 0.70/0.98 (r(s(s(z)), s(s(s(elem!1))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[434, 3761])).
% 0.70/0.98 tff(3763,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3764,plain,
% 0.70/0.98 (((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z))))) <=> ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3765,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3764])).
% 0.70/0.98 tff(3766,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3765, 3763])).
% 0.70/0.98 tff(3767,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3768,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(s(s(elem!1))))) | (~r(s(z), s(s(z)))) | (~r(s(z), s(s(s(elem!1)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3767, 3766])).
% 0.70/0.98 tff(3769,plain,
% 0.70/0.98 (~r(s(z), s(s(z)))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3768, 371, 2596, 3762])).
% 0.70/0.98 tff(3770,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3771,plain,
% 0.70/0.98 (((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3772,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3771])).
% 0.70/0.98 tff(3773,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3772, 3770])).
% 0.70/0.98 tff(3774,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z)))))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3775,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(z)), z)) | (~b(s(z), s(s(z))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3774, 3773])).
% 0.70/0.98 tff(3776,plain,
% 0.70/0.98 (~b(s(z), s(s(z)))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3775, 272, 983, 1308])).
% 0.70/0.98 tff(3777,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[804, 3776, 3769])).
% 0.70/0.98 tff(3778,plain,((~r(s(s(z)), elem!1)) | (~b(s(z), z)) | (~r(s(z), s(s(s(elem!1))))) | (~(s(s(s(s(s(s(elem!1)))))) = s(s(s(elem!1))))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3779,plain,
% 0.70/0.98 (~r(s(s(z)), elem!1)),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3778, 3755, 972, 3751, 1308])).
% 0.70/0.98 tff(3780,plain,
% 0.70/0.98 (b(s(s(z)), elem!1)),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[476, 3779, 3672])).
% 0.70/0.98 tff(3781,assumption,(b(elem!1, s(s(s(z))))), introduced(assumption)).
% 0.70/0.98 tff(3782,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3783,plain,
% 0.70/0.98 (((~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(z)), elem!1))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3784,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3783])).
% 0.70/0.98 tff(3785,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3784, 3782])).
% 0.70/0.98 tff(3786,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(z)), elem!1)))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3787,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3786, 3785])).
% 0.70/0.98 tff(3788,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3787, 272, 326, 3781, 3265])).
% 0.70/0.98 tff(3789,plain,((~b(elem!1, s(s(s(z))))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3790,plain,
% 0.70/0.98 (~b(s(s(z)), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3789, 3781, 326])).
% 0.70/0.98 tff(3791,plain,
% 0.70/0.98 (r(s(s(z)), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3288, 3790])).
% 0.70/0.98 tff(3792,assumption,(r(s(s(z)), s(s(s(z))))), introduced(assumption)).
% 0.70/0.98 tff(3793,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3794,plain,
% 0.70/0.98 (((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3795,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3794])).
% 0.70/0.98 tff(3796,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3795, 3793])).
% 0.70/0.98 tff(3797,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3798,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3797, 3796])).
% 0.70/0.98 tff(3799,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3798, 371, 973, 1521, 3792])).
% 0.70/0.98 tff(3800,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), z)) | (~r(z, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3801,plain,
% 0.70/0.98 (~r(z, s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3800, 3791, 1133])).
% 0.70/0.98 tff(3802,plain,
% 0.70/0.98 (b(z, s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[1541, 3801])).
% 0.70/0.98 tff(3803,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3804,plain,
% 0.70/0.98 (((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3805,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3804])).
% 0.70/0.98 tff(3806,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3805, 3803])).
% 0.70/0.98 tff(3807,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3808,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3807, 3806])).
% 0.70/0.98 tff(3809,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3808, 272, 262, 3781, 3802])).
% 0.70/0.98 tff(3810,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3811,plain,
% 0.70/0.98 (~b(elem!1, s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3810, 3780, 262])).
% 0.70/0.98 tff(3812,plain,
% 0.70/0.98 (r(elem!1, s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[1856, 3811, 3663])).
% 0.70/0.98 tff(3813,assumption,(r(s(z), s(s(s(z))))), introduced(assumption)).
% 0.70/0.98 tff(3814,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3815,plain,
% 0.70/0.98 (((~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))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3816,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3815])).
% 0.70/0.98 tff(3817,plain,
% 0.70/0.98 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3816, 3814])).
% 0.70/0.98 tff(3818,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), elem!1)))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3819,plain,
% 0.70/0.98 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(elem!1, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3818, 3817])).
% 0.70/0.98 tff(3820,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3819, 371, 1101, 1472, 3813])).
% 0.70/0.98 tff(3821,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3822,plain,
% 0.70/0.98 (~r(s(z), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3821, 3812, 3743])).
% 0.70/0.98 tff(3823,plain,
% 0.70/0.98 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3824,plain,
% 0.70/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z)))))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3825,plain,
% 0.70/0.98 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3824, 3823])).
% 0.70/0.98 tff(3826,plain,
% 0.70/0.98 ((s(z) = s(s(s(z)))) | b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3825, 139])).
% 0.70/0.98 tff(3827,plain,
% 0.70/0.98 (b(s(z), s(s(s(z)))) | r(s(z), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3826, 196])).
% 0.70/0.98 tff(3828,plain,
% 0.70/0.98 (b(s(z), s(s(s(z))))),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3827, 3822])).
% 0.70/0.98 tff(3829,assumption,(b(s(s(s(z))), z)), introduced(assumption)).
% 0.70/0.98 tff(3830,assumption,(b(s(z), s(s(s(z))))), introduced(assumption)).
% 0.70/0.98 tff(3831,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3832,plain,
% 0.70/0.98 (((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))) <=> ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.70/0.98 inference(rewrite,[status(thm)],[])).
% 0.70/0.98 tff(3833,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))))),
% 0.70/0.98 inference(monotonicity,[status(thm)],[3832])).
% 0.70/0.98 tff(3834,plain,
% 0.70/0.98 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.70/0.98 inference(transitivity,[status(thm)],[3833, 3831])).
% 0.70/0.98 tff(3835,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z))))))),
% 0.70/0.98 inference(quant_inst,[status(thm)],[])).
% 0.70/0.98 tff(3836,plain,
% 0.70/0.98 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(z))), z)) | (~b(s(z), s(s(s(z)))))),
% 0.70/0.98 inference(modus_ponens,[status(thm)],[3835, 3834])).
% 0.70/0.98 tff(3837,plain,
% 0.70/0.98 ($false),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3836, 272, 1308, 3830, 3829])).
% 0.70/0.98 tff(3838,plain,((~b(s(s(s(z))), z)) | (~b(s(z), z)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.98 tff(3839,plain,
% 0.70/0.98 (~b(s(s(s(z))), z)),
% 0.70/0.98 inference(unit_resolution,[status(thm)],[3838, 3828, 1308])).
% 0.70/0.98 tff(3840,plain,
% 0.70/0.98 (((~![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))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3841,plain,
% 0.70/0.99 ((~![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))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3842,plain,
% 0.70/0.99 ((~![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)),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3841, 3840])).
% 0.70/0.99 tff(3843,plain,
% 0.70/0.99 (b(s(s(s(z))), z) | r(s(s(s(z))), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3842, 139, 1535])).
% 0.70/0.99 tff(3844,plain,
% 0.70/0.99 (r(s(s(s(z))), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3843, 3839])).
% 0.70/0.99 tff(3845,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3846,plain,
% 0.70/0.99 (((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3847,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3846])).
% 0.70/0.99 tff(3848,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z)))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3847, 3845])).
% 0.70/0.99 tff(3849,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3850,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(s(s(s(z))), z))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3849, 3848])).
% 0.70/0.99 tff(3851,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3850, 371, 972, 3812, 3844])).
% 0.70/0.99 tff(3852,plain,((~b(s(z), z)) | (~r(elem!1, z)) | (~b(z, elem!1)) | (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3853,plain,
% 0.70/0.99 (~b(s(z), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3852, 3683, 3682, 3741, 1416])).
% 0.70/0.99 tff(3854,plain,
% 0.70/0.99 (r(s(z), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[289, 3853])).
% 0.70/0.99 tff(3855,plain,
% 0.70/0.99 (s(s(s(elem!1))) = elem!1),
% 0.70/0.99 inference(transitivity,[status(thm)],[3686, 3741])).
% 0.70/0.99 tff(3856,plain,
% 0.70/0.99 (b(s(s(s(elem!1))), s(z)) <=> b(elem!1, s(z))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3855])).
% 0.70/0.99 tff(3857,plain,
% 0.70/0.99 (b(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> b(s(s(s(elem!1))), s(z))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3673])).
% 0.70/0.99 tff(3858,plain,
% 0.70/0.99 (b(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> b(elem!1, s(z))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3857, 3856])).
% 0.70/0.99 tff(3859,plain,
% 0.70/0.99 ((elem!1 = s(elem!1)) <=> (elem!1 = s(s(s(elem!1))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3676])).
% 0.70/0.99 tff(3860,plain,
% 0.70/0.99 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 0.70/0.99 inference(symmetry,[status(thm)],[3859])).
% 0.70/0.99 tff(3861,plain,
% 0.70/0.99 ((s(s(s(s(s(s(s(elem!1))))))) = elem!1) <=> (s(elem!1) = elem!1)),
% 0.70/0.99 inference(transitivity,[status(thm)],[3748, 3860, 1553])).
% 0.70/0.99 tff(3862,plain,
% 0.70/0.99 (s(elem!1) = elem!1),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3741, 3861])).
% 0.70/0.99 tff(3863,plain,
% 0.70/0.99 (r(s(s(s(elem!1))), z) <=> r(s(elem!1), z)),
% 0.70/0.99 inference(symmetry,[status(thm)],[3677])).
% 0.70/0.99 tff(3864,plain,
% 0.70/0.99 (r(s(s(s(elem!1))), z) <=> r(elem!1, z)),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3855])).
% 0.70/0.99 tff(3865,plain,
% 0.70/0.99 (r(elem!1, z) <=> r(s(s(s(elem!1))), z)),
% 0.70/0.99 inference(symmetry,[status(thm)],[3864])).
% 0.70/0.99 tff(3866,plain,
% 0.70/0.99 (r(elem!1, z) <=> r(s(elem!1), z)),
% 0.70/0.99 inference(transitivity,[status(thm)],[3865, 3863])).
% 0.70/0.99 tff(3867,plain,
% 0.70/0.99 (r(s(elem!1), z)),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3683, 3866])).
% 0.70/0.99 tff(3868,plain,
% 0.70/0.99 (~r(s(elem!1), s(z))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[1512, 3854, 3867])).
% 0.70/0.99 tff(3869,plain,
% 0.70/0.99 (r(s(elem!1), s(z)) <=> r(elem!1, s(z))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[238])).
% 0.70/0.99 tff(3870,plain,
% 0.70/0.99 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 0.70/0.99 inference(symmetry,[status(thm)],[3869])).
% 0.70/0.99 tff(3871,plain,
% 0.70/0.99 (s(s(elem!1)) = s(elem!1)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[246, 238])).
% 0.70/0.99 tff(3872,plain,
% 0.70/0.99 (elem!1 = s(s(elem!1))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[98, 3871])).
% 0.70/0.99 tff(3873,plain,
% 0.70/0.99 (s(s(elem!1)) = elem!1),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[235, 3872])).
% 0.70/0.99 tff(3874,plain,
% 0.70/0.99 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[230, 3873])).
% 0.70/0.99 tff(3875,plain,
% 0.70/0.99 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3874])).
% 0.70/0.99 tff(3876,plain,
% 0.70/0.99 (s(s(s(s(s(s(s(elem!1))))))) = elem!1),
% 0.70/0.99 inference(transitivity,[status(thm)],[3875, 238])).
% 0.70/0.99 tff(3877,plain,
% 0.70/0.99 (r(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> r(elem!1, s(z))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3876])).
% 0.70/0.99 tff(3878,plain,
% 0.70/0.99 (r(s(s(s(s(s(s(s(elem!1))))))), s(z)) <=> r(s(elem!1), s(z))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3877, 3870])).
% 0.70/0.99 tff(3879,plain,
% 0.70/0.99 (r(s(elem!1), s(z))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[1999, 3878])).
% 0.70/0.99 tff(3880,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[318, 3879])).
% 0.70/0.99 tff(3881,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(z))) | r(s(elem!1), s(z)) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3882,plain,
% 0.70/0.99 (~r(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3881, 3868, 3862])).
% 0.70/0.99 tff(3883,plain,
% 0.70/0.99 (b(s(s(s(s(s(s(s(elem!1))))))), s(z))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3024, 3882])).
% 0.70/0.99 tff(3884,plain,
% 0.70/0.99 (b(elem!1, s(z))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3883, 3858])).
% 0.70/0.99 tff(3885,plain,
% 0.70/0.99 (~r(s(z), elem!1)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3709, 3854, 3683])).
% 0.70/0.99 tff(3886,plain,
% 0.70/0.99 (b(s(z), elem!1)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[143, 3885, 1416])).
% 0.70/0.99 tff(3887,plain,
% 0.70/0.99 (~b(s(s(z)), elem!1)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3578, 3886, 3682])).
% 0.70/0.99 tff(3888,plain,
% 0.70/0.99 (r(s(s(z)), elem!1)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[476, 3887, 3672])).
% 0.70/0.99 tff(3889,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3890,plain,
% 0.70/0.99 (((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z))) <=> ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3891,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3890])).
% 0.70/0.99 tff(3892,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z))))))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3891, 3889])).
% 0.70/0.99 tff(3893,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, z)))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3894,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z))))) | (~r(z, s(s(s(z)))))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3893, 3892])).
% 0.70/0.99 tff(3895,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3894, 371, 972, 1472, 1521])).
% 0.70/0.99 tff(3896,plain,((~r(z, s(s(s(z))))) | (~r(elem!1, z)) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3897,plain,
% 0.70/0.99 (~r(z, s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3896, 1472, 972])).
% 0.70/0.99 tff(3898,plain,
% 0.70/0.99 (b(z, s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[1541, 3897])).
% 0.70/0.99 tff(3899,plain,
% 0.70/0.99 (~b(s(s(z)), s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3274, 3898, 983])).
% 0.70/0.99 tff(3900,plain,
% 0.70/0.99 (r(s(s(z)), s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3288, 3899])).
% 0.70/0.99 tff(3901,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3902,plain,
% 0.70/0.99 (((~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(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3903,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3902])).
% 0.70/0.99 tff(3904,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3903, 3901])).
% 0.70/0.99 tff(3905,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), elem!1)))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3906,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3905, 3904])).
% 0.70/0.99 tff(3907,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3906, 371, 434, 1472, 3900])).
% 0.70/0.99 tff(3908,plain,((~r(elem!1, s(s(s(z))))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3909,plain,
% 0.70/0.99 (~r(elem!1, s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3908, 3888, 3683])).
% 0.70/0.99 tff(3910,plain,
% 0.70/0.99 (b(elem!1, s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[1856, 3909, 3663])).
% 0.70/0.99 tff(3911,assumption,(b(elem!1, s(z))), introduced(assumption)).
% 0.70/0.99 tff(3912,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3913,plain,
% 0.70/0.99 (((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), 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))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3914,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3913])).
% 0.70/0.99 tff(3915,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3914, 3912])).
% 0.70/0.99 tff(3916,plain,
% 0.70/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3917,plain,
% 0.70/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3916, 3915])).
% 0.70/0.99 tff(3918,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3917, 272, 3911, 3781, 3830])).
% 0.70/0.99 tff(3919,plain,((~b(s(z), s(s(s(z))))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3920,plain,
% 0.70/0.99 (~b(s(z), s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3919, 3910, 3884])).
% 0.70/0.99 tff(3921,plain,
% 0.70/0.99 (r(s(z), s(s(s(z))))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3827, 3920])).
% 0.70/0.99 tff(3922,assumption,(r(s(s(s(z))), z)), introduced(assumption)).
% 0.70/0.99 tff(3923,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3924,plain,
% 0.70/0.99 (((~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))))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3925,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3924])).
% 0.70/0.99 tff(3926,plain,
% 0.70/0.99 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z))))))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3925, 3923])).
% 0.70/0.99 tff(3927,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z))))))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3928,plain,
% 0.70/0.99 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(s(s(s(z))), z)) | (~r(s(z), s(s(s(z)))))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3927, 3926])).
% 0.70/0.99 tff(3929,plain,
% 0.70/0.99 ($false),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3928, 371, 672, 3813, 3922])).
% 0.70/0.99 tff(3930,plain,((~r(s(s(s(z))), z)) | (~r(s(z), z)) | (~r(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/0.99 tff(3931,plain,
% 0.70/0.99 (~r(s(s(s(z))), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3930, 3921, 3854])).
% 0.70/0.99 tff(3932,plain,
% 0.70/0.99 (b(s(s(s(z))), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3843, 3931])).
% 0.70/0.99 tff(3933,plain,
% 0.70/0.99 (~r(s(s(z)), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[981, 3888, 3683])).
% 0.70/0.99 tff(3934,plain,
% 0.70/0.99 (b(s(s(z)), z)),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[462, 3933])).
% 0.70/0.99 tff(3935,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3936,plain,
% 0.70/0.99 (((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3937,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3936])).
% 0.70/0.99 tff(3938,plain,
% 0.70/0.99 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z)))),
% 0.70/0.99 inference(transitivity,[status(thm)],[3937, 3935])).
% 0.70/0.99 tff(3939,plain,
% 0.70/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3940,plain,
% 0.70/0.99 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3939, 3938])).
% 0.70/0.99 tff(3941,plain,
% 0.70/0.99 (~b(s(s(s(z))), s(s(z)))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3940, 272, 3934, 3932])).
% 0.70/0.99 tff(3942,plain,
% 0.70/0.99 ((s(s(s(z))) = s(s(z))) <=> (s(s(z)) = s(s(s(z))))),
% 0.70/0.99 inference(commutativity,[status(thm)],[])).
% 0.70/0.99 tff(3943,plain,
% 0.70/0.99 ((s(s(z)) = s(s(s(z)))) <=> (s(s(s(z))) = s(s(z)))),
% 0.70/0.99 inference(symmetry,[status(thm)],[3942])).
% 0.70/0.99 tff(3944,plain,
% 0.70/0.99 ((~(s(s(z)) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(s(z))))),
% 0.70/0.99 inference(monotonicity,[status(thm)],[3943])).
% 0.70/0.99 tff(3945,plain,
% 0.70/0.99 (~(s(s(s(z))) = s(s(z)))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3283, 3944])).
% 0.70/0.99 tff(3946,plain,
% 0.70/0.99 (((~![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))))),
% 0.70/0.99 inference(rewrite,[status(thm)],[])).
% 0.70/0.99 tff(3947,plain,
% 0.70/0.99 ((~![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))))),
% 0.70/0.99 inference(quant_inst,[status(thm)],[])).
% 0.70/0.99 tff(3948,plain,
% 0.70/0.99 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.70/0.99 inference(modus_ponens,[status(thm)],[3947, 3946])).
% 0.70/0.99 tff(3949,plain,
% 0.70/0.99 ((s(s(s(z))) = s(s(z))) | b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3948, 139])).
% 0.70/0.99 tff(3950,plain,
% 0.70/0.99 (b(s(s(s(z))), s(s(z))) | r(s(s(s(z))), s(s(z)))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3949, 3945])).
% 0.70/0.99 tff(3951,plain,
% 0.70/0.99 (r(s(s(s(z))), s(s(z)))),
% 0.70/0.99 inference(unit_resolution,[status(thm)],[3950, 3941])).
% 0.70/0.99 tff(3952,plain,
% 0.70/0.99 ((elem!1 = s(s(z))) <=> (s(s(z)) = elem!1)),
% 0.70/0.99 inference(commutativity,[status(thm)],[])).
% 0.70/0.99 tff(3953,assumption,(elem!1 = s(s(z))), introduced(assumption)).
% 0.70/1.00 tff(3954,plain,
% 0.70/1.00 (s(s(z)) = elem!1),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3953, 3952])).
% 0.70/1.00 tff(3955,plain,
% 0.70/1.00 ($false),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[1346, 3954])).
% 0.70/1.00 tff(3956,plain,((~(elem!1 = s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/1.00 tff(3957,plain,
% 0.70/1.00 (~(elem!1 = s(s(z)))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3956, 3672])).
% 0.70/1.00 tff(3958,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3959,plain,
% 0.70/1.00 (((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3960,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[3959])).
% 0.70/1.00 tff(3961,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.00 inference(transitivity,[status(thm)],[3960, 3958])).
% 0.70/1.00 tff(3962,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3963,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(z)), s(s(s(z)))))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3962, 3961])).
% 0.70/1.00 tff(3964,plain,
% 0.70/1.00 (~b(s(s(z)), s(s(s(z))))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3963, 272, 3934, 3932])).
% 0.70/1.00 tff(3965,plain,
% 0.70/1.00 (r(s(s(z)), s(s(s(z))))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3288, 3964])).
% 0.70/1.00 tff(3966,plain,
% 0.70/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3967,plain,
% 0.70/1.00 (((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z)))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3968,plain,
% 0.70/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[3967])).
% 0.70/1.00 tff(3969,plain,
% 0.70/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.70/1.00 inference(transitivity,[status(thm)],[3968, 3966])).
% 0.70/1.00 tff(3970,plain,
% 0.70/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(s(z))))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(z)), s(z))))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3971,plain,
% 0.70/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3970, 3969])).
% 0.70/1.00 tff(3972,plain,
% 0.70/1.00 (~r(s(s(z)), s(z))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3971, 371, 3965, 3921])).
% 0.70/1.00 tff(3973,plain,
% 0.70/1.00 (b(s(s(z)), s(z))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[359, 3972])).
% 0.70/1.00 tff(3974,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3975,plain,
% 0.70/1.00 (((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z))))) <=> ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3976,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z)))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[3975])).
% 0.70/1.00 tff(3977,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z))))),
% 0.70/1.00 inference(transitivity,[status(thm)],[3976, 3974])).
% 0.70/1.00 tff(3978,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(elem!1, s(z))) | (~b(s(s(z)), s(z))) | (~b(elem!1, s(s(z)))))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3979,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(z))) | (~b(elem!1, s(s(z)))) | (~b(s(s(z)), s(z)))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3978, 3977])).
% 0.70/1.00 tff(3980,plain,
% 0.70/1.00 (~b(elem!1, s(s(z)))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3979, 272, 3884, 3973])).
% 0.70/1.00 tff(3981,plain,
% 0.70/1.00 (((~![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))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3982,plain,
% 0.70/1.00 ((~![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))))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3983,plain,
% 0.70/1.00 ((~![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)))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3982, 3981])).
% 0.70/1.00 tff(3984,plain,
% 0.70/1.00 ((elem!1 = s(s(z))) | b(elem!1, s(s(z))) | r(elem!1, s(s(z)))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3983, 139])).
% 0.70/1.00 tff(3985,plain,
% 0.70/1.00 (r(elem!1, s(s(z)))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3984, 3980, 3957])).
% 0.70/1.00 tff(3986,plain,
% 0.70/1.00 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3987,plain,
% 0.70/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3988,plain,
% 0.70/1.00 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), elem!1))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3987, 3986])).
% 0.70/1.00 tff(3989,plain,
% 0.70/1.00 (~r(s(s(s(z))), elem!1)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3988, 371, 3985, 3951])).
% 0.70/1.00 tff(3990,plain,
% 0.70/1.00 (((~![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))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3991,plain,
% 0.70/1.00 ((~![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))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(3992,plain,
% 0.70/1.00 ((~![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)),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3991, 3990])).
% 0.70/1.00 tff(3993,plain,
% 0.70/1.00 ((s(s(s(z))) = elem!1) | b(s(s(s(z))), elem!1) | r(s(s(s(z))), elem!1)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3992, 139])).
% 0.70/1.00 tff(3994,plain,
% 0.70/1.00 (b(s(s(s(z))), elem!1)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3993, 3989, 3670])).
% 0.70/1.00 tff(3995,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3996,plain,
% 0.70/1.00 (((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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)))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(3997,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[3996])).
% 0.70/1.00 tff(3998,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1)))),
% 0.70/1.00 inference(transitivity,[status(thm)],[3997, 3995])).
% 0.70/1.00 tff(3999,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(4000,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(z))), elem!1))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[3999, 3998])).
% 0.70/1.00 tff(4001,plain,
% 0.70/1.00 ($false),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[4000, 272, 3682, 3994, 3932])).
% 0.70/1.00 tff(4002,plain,(b(elem!1, z) | (s(z) = elem!1) | r(z, elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.70/1.00 tff(4003,plain,
% 0.70/1.00 (b(elem!1, z)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[4002, 1416, 1936, 52])).
% 0.70/1.00 tff(4004,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(4005,plain,
% 0.70/1.00 (((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))) <=> ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(4006,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[4005])).
% 0.70/1.00 tff(4007,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(transitivity,[status(thm)],[4006, 4004])).
% 0.70/1.00 tff(4008,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(quant_inst,[status(thm)],[])).
% 0.70/1.00 tff(4009,plain,
% 0.70/1.00 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(s(s(z))), z)) | (~b(elem!1, s(s(s(z)))))),
% 0.70/1.00 inference(modus_ponens,[status(thm)],[4008, 4007])).
% 0.70/1.00 tff(4010,plain,
% 0.70/1.00 ($false),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[4009, 272, 1032, 3781, 3829])).
% 0.70/1.00 tff(4011,plain,((~b(s(s(s(z))), z)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.00 tff(4012,plain,
% 0.70/1.00 (~b(s(s(s(z))), z)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[4011, 3781, 1032])).
% 0.70/1.00 tff(4013,plain,
% 0.70/1.00 (r(s(s(s(z))), z)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3843, 4012])).
% 0.70/1.00 tff(4014,plain,
% 0.70/1.00 (~b(s(z), z)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[1005, 253, 1032])).
% 0.70/1.00 tff(4015,plain,
% 0.70/1.00 (r(s(z), z)),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[289, 4014])).
% 0.70/1.00 tff(4016,plain,
% 0.70/1.00 (~r(s(z), s(s(s(z))))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3930, 4015, 4013])).
% 0.70/1.00 tff(4017,plain,
% 0.70/1.00 (b(s(z), s(s(s(z))))),
% 0.70/1.00 inference(unit_resolution,[status(thm)],[3827, 4016])).
% 0.70/1.00 tff(4018,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(4019,plain,
% 0.70/1.00 (((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), elem!1))) <=> ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.00 inference(rewrite,[status(thm)],[])).
% 0.70/1.00 tff(4020,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))))),
% 0.70/1.00 inference(monotonicity,[status(thm)],[4019])).
% 0.70/1.00 tff(4021,plain,
% 0.70/1.00 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z))))))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4020, 4018])).
% 0.70/1.01 tff(4022,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, z)) | (~b(s(z), elem!1)))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4023,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(elem!1, s(s(s(z)))))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4022, 4021])).
% 0.70/1.01 tff(4024,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4023, 272, 1032, 253, 3781, 4017])).
% 0.70/1.01 tff(4025,plain,((~b(s(z), elem!1)) | (~b(elem!1, z)) | (~b(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4026,plain,
% 0.70/1.01 (~b(s(z), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4025, 3781, 1032])).
% 0.70/1.01 tff(4027,plain,
% 0.70/1.01 (r(s(z), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[143, 4026, 1416])).
% 0.70/1.01 tff(4028,plain,
% 0.70/1.01 (~b(s(s(z)), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[3810, 3781, 262])).
% 0.70/1.01 tff(4029,plain,
% 0.70/1.01 (r(s(s(z)), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[476, 4028, 3672])).
% 0.70/1.01 tff(4030,plain,
% 0.70/1.01 (~r(s(s(z)), s(z))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[1111, 371, 4029, 4027])).
% 0.70/1.01 tff(4031,plain,
% 0.70/1.01 (b(s(s(z)), s(z))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[359, 4030])).
% 0.70/1.01 tff(4032,assumption,(r(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.70/1.01 tff(4033,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4034,plain,
% 0.70/1.01 (((~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(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4035,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4034])).
% 0.70/1.01 tff(4036,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4035, 4033])).
% 0.70/1.01 tff(4037,plain,
% 0.70/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4038,plain,
% 0.70/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4037, 4036])).
% 0.70/1.01 tff(4039,plain,
% 0.70/1.01 (~r(s(z), s(s(s(s(z)))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4038, 371, 1101, 4032])).
% 0.70/1.01 tff(4040,assumption,(s(z) = s(s(s(s(z))))), introduced(assumption)).
% 0.70/1.01 tff(4041,plain,
% 0.70/1.01 (inj_0(s(z)) = inj_0(s(s(s(s(z)))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4040])).
% 0.70/1.01 tff(4042,plain,
% 0.70/1.01 (inj_0(s(s(s(s(z))))) = inj_0(s(z))),
% 0.70/1.01 inference(symmetry,[status(thm)],[4041])).
% 0.70/1.01 tff(4043,plain,
% 0.70/1.01 (s(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.70/1.01 inference(symmetry,[status(thm)],[3609])).
% 0.70/1.01 tff(4044,plain,
% 0.70/1.01 (s(s(s(z))) = z),
% 0.70/1.01 inference(transitivity,[status(thm)],[4043, 4042, 24])).
% 0.70/1.01 tff(4045,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[1535, 4044])).
% 0.70/1.01 tff(4046,plain,(~(s(z) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4047,plain,
% 0.70/1.01 (((~![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))))))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4048,plain,
% 0.70/1.01 ((~![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))))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4049,plain,
% 0.70/1.01 ((~![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)))))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4048, 4047])).
% 0.70/1.01 tff(4050,plain,
% 0.70/1.01 (b(s(z), s(s(s(s(z)))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4049, 139, 4046, 4039])).
% 0.70/1.01 tff(4051,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4052,plain,
% 0.70/1.01 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4053,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4052])).
% 0.70/1.01 tff(4054,plain,
% 0.70/1.01 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4053, 4051])).
% 0.70/1.01 tff(4055,plain,
% 0.70/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4056,plain,
% 0.70/1.01 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), elem!1))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4055, 4054])).
% 0.70/1.01 tff(4057,plain,
% 0.70/1.01 (~r(s(s(z)), s(s(s(s(z)))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4056, 371, 434, 4032])).
% 0.70/1.01 tff(4058,assumption,(s(s(z)) = s(s(s(s(z))))), introduced(assumption)).
% 0.70/1.01 tff(4059,plain,
% 0.70/1.01 (inj_0(s(s(z))) = inj_0(s(s(s(s(z)))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4058])).
% 0.70/1.01 tff(4060,plain,
% 0.70/1.01 (s(z) = s(s(s(z)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[213, 4059, 3609])).
% 0.70/1.01 tff(4061,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[196, 4060])).
% 0.70/1.01 tff(4062,plain,(~(s(s(z)) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4063,plain,
% 0.70/1.01 (((~![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))))))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4064,plain,
% 0.70/1.01 ((~![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))))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4065,plain,
% 0.70/1.01 ((~![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)))))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4064, 4063])).
% 0.70/1.01 tff(4066,plain,
% 0.70/1.01 (b(s(s(z)), s(s(s(s(z)))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4065, 139, 4062, 4057])).
% 0.70/1.01 tff(4067,plain,
% 0.70/1.01 (~r(s(z), s(s(z)))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[1359, 371, 434, 1101])).
% 0.70/1.01 tff(4068,plain,
% 0.70/1.01 (b(s(z), s(s(z)))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[804, 4067])).
% 0.70/1.01 tff(4069,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4070,plain,
% 0.70/1.01 (((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z))))) <=> ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4071,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4070])).
% 0.70/1.01 tff(4072,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4071, 4069])).
% 0.70/1.01 tff(4073,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(z)))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4074,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4073, 4072])).
% 0.70/1.01 tff(4075,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4074, 272, 4068, 4066, 4050])).
% 0.70/1.01 tff(4076,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4077,plain,
% 0.70/1.01 (~r(s(s(s(s(z)))), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4076, 4027, 4029])).
% 0.70/1.01 tff(4078,plain,
% 0.70/1.01 (s(s(elem!1)) = elem!1),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[3605, 248])).
% 0.70/1.01 tff(4079,plain,
% 0.70/1.01 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[3624, 3409, 4078])).
% 0.70/1.01 tff(4080,plain,
% 0.70/1.01 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[2232, 4079])).
% 0.70/1.01 tff(4081,plain,
% 0.70/1.01 (~(s(elem!1) = s(z))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[50, 4080])).
% 0.70/1.01 tff(4082,plain,
% 0.70/1.01 (~b(s(elem!1), s(z))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[1121, 1101, 248, 434, 637])).
% 0.70/1.01 tff(4083,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[324, 4082, 1899, 4081])).
% 0.70/1.01 tff(4084,plain,((~r(s(z), elem!1)) | (s(elem!1) = s(s(z))) | (~r(s(s(z)), elem!1)) | (~r(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4085,plain,
% 0.70/1.01 (~r(s(elem!1), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4084, 4027, 4029, 3643])).
% 0.70/1.01 tff(4086,plain,
% 0.70/1.01 (s(elem!1) = elem!1),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[618, 4085, 52])).
% 0.70/1.01 tff(4087,plain,
% 0.70/1.01 (elem!1 = s(elem!1)),
% 0.70/1.01 inference(symmetry,[status(thm)],[238])).
% 0.70/1.01 tff(4088,plain,
% 0.70/1.01 (elem!1 = s(s(s(z)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4087, 68, 3617, 3613, 3609])).
% 0.70/1.01 tff(4089,plain,
% 0.70/1.01 (~(elem!1 = s(s(s(z))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[3662, 222])).
% 0.70/1.01 tff(4090,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4089, 4088])).
% 0.70/1.01 tff(4091,plain,((~(s(s(s(s(z)))) = elem!1)) | (~(s(elem!1) = elem!1)) | (~(s(s(elem!1)) = elem!1)) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4092,plain,
% 0.70/1.01 (~(s(s(s(s(z)))) = elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4091, 4086, 3644, 3671])).
% 0.70/1.01 tff(4093,plain,
% 0.70/1.01 (((~![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))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4094,plain,
% 0.70/1.01 ((~![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))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4095,plain,
% 0.70/1.01 ((~![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)),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4094, 4093])).
% 0.70/1.01 tff(4096,plain,
% 0.70/1.01 ((s(s(s(s(z)))) = elem!1) | b(s(s(s(s(z)))), elem!1) | r(s(s(s(s(z)))), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4095, 139])).
% 0.70/1.01 tff(4097,plain,
% 0.70/1.01 (b(s(s(s(s(z)))), elem!1)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4096, 4092, 4077])).
% 0.70/1.01 tff(4098,assumption,(b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.70/1.01 tff(4099,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4100,plain,
% 0.70/1.01 (((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z))) <=> ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4101,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4100])).
% 0.70/1.01 tff(4102,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4101, 4099])).
% 0.70/1.01 tff(4103,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4104,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(s(z)))), elem!1))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4103, 4102])).
% 0.70/1.01 tff(4105,plain,
% 0.70/1.01 (~b(s(s(s(s(z)))), z)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4104, 272, 262, 4098])).
% 0.70/1.01 tff(4106,plain,
% 0.70/1.01 ((~![X: $i] : (~(s(X) = z))) | (~(s(s(s(s(z)))) = z))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4107,plain,
% 0.70/1.01 (~(s(s(s(s(z)))) = z)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4106, 46])).
% 0.70/1.01 tff(4108,plain,
% 0.70/1.01 (((~![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))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4109,plain,
% 0.70/1.01 ((~![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))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4110,plain,
% 0.70/1.01 ((~![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)),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4109, 4108])).
% 0.70/1.01 tff(4111,plain,
% 0.70/1.01 (r(s(s(s(s(z)))), z)),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4110, 139, 4107, 4105])).
% 0.70/1.01 tff(4112,assumption,(b(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.70/1.01 tff(4113,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4114,plain,
% 0.70/1.01 (((~b(s(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(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(rewrite,[status(thm)],[])).
% 0.70/1.01 tff(4115,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4114])).
% 0.70/1.01 tff(4116,plain,
% 0.70/1.01 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.01 inference(transitivity,[status(thm)],[4115, 4113])).
% 0.70/1.01 tff(4117,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(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)))))))),
% 0.70/1.01 inference(quant_inst,[status(thm)],[])).
% 0.70/1.01 tff(4118,plain,
% 0.70/1.01 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 0.70/1.01 inference(modus_ponens,[status(thm)],[4117, 4116])).
% 0.70/1.01 tff(4119,plain,
% 0.70/1.01 (~b(s(s(s(z))), s(s(s(s(z)))))),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4118, 272, 4112, 4098])).
% 0.70/1.01 tff(4120,assumption,(s(s(s(z))) = s(s(s(s(z))))), introduced(assumption)).
% 0.70/1.01 tff(4121,plain,
% 0.70/1.01 (inj_0(s(s(s(z)))) = inj_0(s(s(s(s(z)))))),
% 0.70/1.01 inference(monotonicity,[status(thm)],[4120])).
% 0.70/1.01 tff(4122,plain,
% 0.70/1.01 (s(s(z)) = s(s(s(s(z))))),
% 0.70/1.01 inference(transitivity,[status(thm)],[191, 4121, 3609, 4120])).
% 0.70/1.01 tff(4123,plain,
% 0.70/1.01 ($false),
% 0.70/1.01 inference(unit_resolution,[status(thm)],[4062, 4122])).
% 0.70/1.01 tff(4124,plain,(~(s(s(s(z))) = s(s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.01 tff(4125,plain,
% 0.70/1.01 (((~![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))))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4126,plain,
% 0.70/1.02 ((~![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))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4127,plain,
% 0.70/1.02 ((~![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)))))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4126, 4125])).
% 0.70/1.02 tff(4128,plain,
% 0.70/1.02 (r(s(s(s(z))), s(s(s(s(z)))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4127, 139, 4124, 4119])).
% 0.70/1.02 tff(4129,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4130,plain,
% 0.70/1.02 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4131,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4130])).
% 0.70/1.02 tff(4132,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4131, 4129])).
% 0.70/1.02 tff(4133,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4134,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), z)) | (~r(s(s(s(z))), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4133, 4132])).
% 0.70/1.02 tff(4135,plain,
% 0.70/1.02 ($false),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4134, 371, 3922, 4128, 4111])).
% 0.70/1.02 tff(4136,plain,((~b(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), z)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.02 tff(4137,plain,
% 0.70/1.02 (~b(s(s(s(z))), elem!1)),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4136, 4097, 262, 4013])).
% 0.70/1.02 tff(4138,plain,
% 0.70/1.02 (r(s(s(s(z))), elem!1)),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3993, 4137, 3670])).
% 0.70/1.02 tff(4139,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4140,plain,
% 0.70/1.02 (((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z)))))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4141,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4140])).
% 0.70/1.02 tff(4142,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4141, 4139])).
% 0.70/1.02 tff(4143,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4144,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4143, 4142])).
% 0.70/1.02 tff(4145,plain,
% 0.70/1.02 (~r(s(s(z)), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4144, 371, 4029, 4138])).
% 0.70/1.02 tff(4146,plain,
% 0.70/1.02 (b(s(s(z)), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3288, 4145])).
% 0.70/1.02 tff(4147,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4148,plain,
% 0.70/1.02 (((~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(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4149,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4148])).
% 0.70/1.02 tff(4150,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4149, 4147])).
% 0.70/1.02 tff(4151,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4152,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(z))))) | (~r(s(s(s(z))), elem!1))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4151, 4150])).
% 0.70/1.02 tff(4153,plain,
% 0.70/1.02 (~r(s(z), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4152, 371, 4027, 4138])).
% 0.70/1.02 tff(4154,plain,
% 0.70/1.02 (b(s(z), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3827, 4153])).
% 0.70/1.02 tff(4155,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4156,plain,
% 0.70/1.02 (((~b(s(z), s(s(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(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4157,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4156])).
% 0.70/1.02 tff(4158,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4157, 4155])).
% 0.70/1.02 tff(4159,plain,
% 0.70/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4160,plain,
% 0.70/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), s(z))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4159, 4158])).
% 0.70/1.02 tff(4161,plain,
% 0.70/1.02 ($false),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4160, 272, 3440, 3265, 3830])).
% 0.70/1.02 tff(4162,plain,((~b(s(z), s(s(s(z))))) | (~b(s(s(z)), s(z))) | (~b(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.02 tff(4163,plain,
% 0.70/1.02 ($false),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4162, 4154, 4146, 4031])).
% 0.70/1.02 tff(4164,plain,((~b(elem!1, s(s(s(z))))) | (~b(z, elem!1)) | b(s(elem!1), elem!1) | (s(z) = elem!1) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.02 tff(4165,plain,
% 0.70/1.02 (~b(elem!1, s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4164, 3682, 52, 1416, 4003])).
% 0.70/1.02 tff(4166,plain,
% 0.70/1.02 (r(elem!1, s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[1856, 4165, 3663])).
% 0.70/1.02 tff(4167,plain,
% 0.70/1.02 (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)),
% 0.70/1.02 inference(monotonicity,[status(thm)],[3671])).
% 0.70/1.02 tff(4168,plain,
% 0.70/1.02 (s(elem!1) = s(s(s(s(s(s(s(elem!1)))))))),
% 0.70/1.02 inference(symmetry,[status(thm)],[4167])).
% 0.70/1.02 tff(4169,plain,
% 0.70/1.02 (s(elem!1) = s(s(s(elem!1)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4168, 3673])).
% 0.70/1.02 tff(4170,plain,
% 0.70/1.02 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4169])).
% 0.70/1.02 tff(4171,plain,
% 0.70/1.02 ((~b(s(elem!1), elem!1)) <=> (~b(s(s(s(elem!1))), elem!1))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4170])).
% 0.70/1.02 tff(4172,plain,
% 0.70/1.02 (~b(s(s(s(elem!1))), elem!1)),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[52, 4171])).
% 0.70/1.02 tff(4173,plain,
% 0.70/1.02 (~b(s(z), elem!1)),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3578, 326, 262])).
% 0.70/1.02 tff(4174,plain,
% 0.70/1.02 (r(s(z), elem!1)),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[143, 4173, 1416])).
% 0.70/1.02 tff(4175,plain,
% 0.70/1.02 (~r(s(z), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3821, 4174, 1472])).
% 0.70/1.02 tff(4176,plain,
% 0.70/1.02 (b(s(z), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[3827, 4175])).
% 0.70/1.02 tff(4177,assumption,(~b(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.70/1.02 tff(4178,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4179,plain,
% 0.70/1.02 (((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4180,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4179])).
% 0.70/1.02 tff(4181,plain,
% 0.70/1.02 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4180, 4178])).
% 0.70/1.02 tff(4182,plain,
% 0.70/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4183,plain,
% 0.70/1.02 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), elem!1))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4182, 4181])).
% 0.70/1.02 tff(4184,plain,
% 0.70/1.02 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4183, 272, 326, 4098])).
% 0.70/1.02 tff(4185,plain,
% 0.70/1.02 (r(s(s(z)), s(s(s(s(z)))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4065, 139, 4062, 4184])).
% 0.70/1.02 tff(4186,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4187,plain,
% 0.70/1.02 (((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4188,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4187])).
% 0.70/1.02 tff(4189,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4188, 4186])).
% 0.70/1.02 tff(4190,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), z)) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4191,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), z)) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), z))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4190, 4189])).
% 0.70/1.02 tff(4192,plain,
% 0.70/1.02 ($false),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4191, 371, 1133, 4185, 4111])).
% 0.70/1.02 tff(4193,plain,((~b(s(s(s(s(z)))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.70/1.02 tff(4194,plain,
% 0.70/1.02 (~b(s(s(s(s(z)))), elem!1)),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4193, 326, 262])).
% 0.70/1.02 tff(4195,plain,
% 0.70/1.02 ((s(s(elem!1)) = s(elem!1)) <=> (s(elem!1) = s(s(elem!1)))),
% 0.70/1.02 inference(symmetry,[status(thm)],[59])).
% 0.70/1.02 tff(4196,plain,
% 0.70/1.02 ((elem!1 = s(elem!1)) <=> (s(s(elem!1)) = s(elem!1))),
% 0.70/1.02 inference(symmetry,[status(thm)],[3701])).
% 0.70/1.02 tff(4197,plain,
% 0.70/1.02 ((elem!1 = s(s(s(elem!1)))) <=> (elem!1 = s(elem!1))),
% 0.70/1.02 inference(symmetry,[status(thm)],[3700])).
% 0.70/1.02 tff(4198,plain,
% 0.70/1.02 ((s(s(s(elem!1))) = elem!1) <=> (s(elem!1) = s(s(elem!1)))),
% 0.70/1.02 inference(transitivity,[status(thm)],[2406, 4197, 4196, 4195])).
% 0.70/1.02 tff(4199,assumption,(r(s(s(s(z))), elem!1)), introduced(assumption)).
% 0.70/1.02 tff(4200,assumption,(r(s(s(s(elem!1))), elem!1)), introduced(assumption)).
% 0.70/1.02 tff(4201,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4202,plain,
% 0.70/1.02 (((~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(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4203,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))))),
% 0.70/1.02 inference(monotonicity,[status(thm)],[4202])).
% 0.70/1.02 tff(4204,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z))))))),
% 0.70/1.02 inference(transitivity,[status(thm)],[4203, 4201])).
% 0.70/1.02 tff(4205,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~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(s(s(s(elem!1))), s(s(s(z))))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4206,plain,
% 0.70/1.02 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(elem!1))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(elem!1))), s(s(s(z)))))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4205, 4204])).
% 0.70/1.02 tff(4207,plain,
% 0.70/1.02 (~r(s(s(s(elem!1))), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4206, 371, 4200, 4199])).
% 0.70/1.02 tff(4208,assumption,(~(s(s(s(elem!1))) = s(s(s(z))))), introduced(assumption)).
% 0.70/1.02 tff(4209,plain,
% 0.70/1.02 (((~![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)))))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4210,plain,
% 0.70/1.02 ((~![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)))))),
% 0.70/1.02 inference(quant_inst,[status(thm)],[])).
% 0.70/1.02 tff(4211,plain,
% 0.70/1.02 ((~![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))))),
% 0.70/1.02 inference(modus_ponens,[status(thm)],[4210, 4209])).
% 0.70/1.02 tff(4212,plain,
% 0.70/1.02 (b(s(s(s(elem!1))), s(s(s(z))))),
% 0.70/1.02 inference(unit_resolution,[status(thm)],[4211, 139, 4208, 4207])).
% 0.70/1.02 tff(4213,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4214,plain,
% 0.70/1.02 (((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1)))))) <=> ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.70/1.02 inference(rewrite,[status(thm)],[])).
% 0.70/1.02 tff(4215,plain,
% 0.70/1.02 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4214])).
% 0.82/1.03 tff(4216,plain,
% 0.82/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[4215, 4213])).
% 0.82/1.03 tff(4217,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(elem!1))), elem!1)) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4218,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), elem!1)) | (~r(s(z), s(s(s(elem!1))))) | (~r(s(s(s(elem!1))), elem!1))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4217, 4216])).
% 0.82/1.03 tff(4219,plain,
% 0.82/1.03 (~r(s(z), s(s(s(elem!1))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4218, 371, 1101, 4200])).
% 0.82/1.03 tff(4220,plain,
% 0.82/1.03 (b(s(z), s(s(s(elem!1))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[2592, 4219])).
% 0.82/1.03 tff(4221,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4222,plain,
% 0.82/1.03 (((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1)))))) <=> ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4223,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4222])).
% 0.82/1.03 tff(4224,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))))),
% 0.82/1.03 inference(transitivity,[status(thm)],[4223, 4221])).
% 0.82/1.03 tff(4225,plain,
% 0.82/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z))))) | (~b(s(z), s(s(s(elem!1))))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4226,plain,
% 0.82/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(s(elem!1))))) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(elem!1))), s(s(s(z)))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4225, 4224])).
% 0.82/1.03 tff(4227,plain,
% 0.82/1.03 ($false),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4226, 272, 4220, 3830, 4212])).
% 0.82/1.03 tff(4228,plain,((~r(s(s(s(elem!1))), elem!1)) | (~b(s(z), s(s(s(z))))) | (s(s(s(elem!1))) = s(s(s(z)))) | (~r(s(z), elem!1)) | (~r(s(s(s(z))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.03 tff(4229,plain,
% 0.82/1.03 (~r(s(s(s(elem!1))), elem!1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4228, 4199, 3635, 1101, 3830])).
% 0.82/1.03 tff(4230,plain,
% 0.82/1.03 (((~![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))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4231,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4232,plain,
% 0.82/1.03 ((~![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)),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4231, 4230])).
% 0.82/1.03 tff(4233,plain,
% 0.82/1.03 ((s(s(s(elem!1))) = elem!1) | b(s(s(s(elem!1))), elem!1) | r(s(s(s(elem!1))), elem!1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4232, 139])).
% 0.82/1.03 tff(4234,plain,
% 0.82/1.03 (s(s(s(elem!1))) = elem!1),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4233, 4229, 4177])).
% 0.82/1.03 tff(4235,plain,
% 0.82/1.03 (s(elem!1) = s(s(elem!1))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4234, 4198])).
% 0.82/1.03 tff(4236,assumption,(~b(s(s(s(s(z)))), elem!1)), introduced(assumption)).
% 0.82/1.03 tff(4237,plain,
% 0.82/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4238,plain,
% 0.82/1.03 (((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4239,plain,
% 0.82/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4238])).
% 0.82/1.03 tff(4240,plain,
% 0.82/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.03 inference(transitivity,[status(thm)],[4239, 4237])).
% 0.82/1.03 tff(4241,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4242,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4241, 4240])).
% 0.82/1.03 tff(4243,plain,
% 0.82/1.03 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4242, 371, 4199, 4032])).
% 0.82/1.03 tff(4244,plain,
% 0.82/1.03 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4127, 139, 4124, 4243])).
% 0.82/1.03 tff(4245,plain,
% 0.82/1.03 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4246,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~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))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4247,plain,
% 0.82/1.03 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4246, 4245])).
% 0.82/1.03 tff(4248,plain,
% 0.82/1.03 (~r(s(s(s(z))), s(z))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4247, 371, 1101, 4199])).
% 0.82/1.03 tff(4249,plain,
% 0.82/1.03 ((s(s(s(z))) = s(z)) <=> (s(z) = s(s(s(z))))),
% 0.82/1.03 inference(commutativity,[status(thm)],[])).
% 0.82/1.03 tff(4250,plain,
% 0.82/1.03 ((s(z) = s(s(s(z)))) <=> (s(s(s(z))) = s(z))),
% 0.82/1.03 inference(symmetry,[status(thm)],[4249])).
% 0.82/1.03 tff(4251,plain,
% 0.82/1.03 ((~(s(z) = s(s(s(z))))) <=> (~(s(s(s(z))) = s(z)))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4250])).
% 0.82/1.03 tff(4252,plain,
% 0.82/1.03 (~(s(s(s(z))) = s(z))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[196, 4251])).
% 0.82/1.03 tff(4253,plain,
% 0.82/1.03 (((~![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)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4254,plain,
% 0.82/1.03 ((~![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)))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4255,plain,
% 0.82/1.03 ((~![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))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4254, 4253])).
% 0.82/1.03 tff(4256,plain,
% 0.82/1.03 ((s(s(s(z))) = s(z)) | b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4255, 139])).
% 0.82/1.03 tff(4257,plain,
% 0.82/1.03 (b(s(s(s(z))), s(z)) | r(s(s(s(z))), s(z))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4256, 4252])).
% 0.82/1.03 tff(4258,plain,
% 0.82/1.03 (b(s(s(s(z))), s(z))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4257, 4248])).
% 0.82/1.03 tff(4259,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4260,plain,
% 0.82/1.03 (((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z)))) <=> ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4261,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z))))))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4260])).
% 0.82/1.03 tff(4262,plain,
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% 0.82/1.03 inference(transitivity,[status(thm)],[4261, 4259])).
% 0.82/1.03 tff(4263,plain,
% 0.82/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(s(s(s(z)))))) | (~b(s(z), s(s(s(s(z)))))) | (~b(s(s(s(z))), s(z))))),
% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4264,plain,
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% 0.82/1.03 inference(modus_ponens,[status(thm)],[4263, 4262])).
% 0.82/1.03 tff(4265,plain,
% 0.82/1.03 ($false),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4264, 272, 4258, 4050, 4244])).
% 0.82/1.03 tff(4266,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.03 tff(4267,plain,
% 0.82/1.03 (~r(s(s(s(s(z)))), elem!1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4266, 4199, 1101])).
% 0.82/1.03 tff(4268,plain,
% 0.82/1.03 (s(s(s(s(z)))) = elem!1),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4096, 4267, 4236])).
% 0.82/1.03 tff(4269,plain,
% 0.82/1.03 (~(s(elem!1) = elem!1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4091, 4268, 222, 207])).
% 0.82/1.03 tff(4270,plain,
% 0.82/1.03 (~(elem!1 = s(elem!1))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1558, 4269])).
% 0.82/1.03 tff(4271,plain,
% 0.82/1.03 (~(s(s(elem!1)) = s(elem!1))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[93, 4270])).
% 0.82/1.03 tff(4272,plain,
% 0.82/1.03 (~(s(elem!1) = s(s(elem!1)))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[623, 4271])).
% 0.82/1.03 tff(4273,plain,
% 0.82/1.03 ($false),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4272, 4235])).
% 0.82/1.03 tff(4274,plain,((~r(s(s(s(z))), elem!1)) | (~(s(s(s(s(s(s(elem!1)))))) = elem!1)) | (~(s(s(elem!1)) = elem!1)) | b(s(s(s(s(z)))), elem!1) | b(s(s(s(elem!1))), elem!1) | (~r(s(z), elem!1)) | (~b(s(z), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.03 tff(4275,plain,
% 0.82/1.03 (~r(s(s(s(z))), elem!1)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4274, 4194, 3644, 3671, 4177, 4174, 4176])).
% 0.82/1.03 tff(4276,plain,
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% 0.82/1.03 inference(unit_resolution,[status(thm)],[3993, 4275, 3670])).
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% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4278,plain,
% 0.82/1.03 (((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z)))))) <=> ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4279,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 0.82/1.03 inference(monotonicity,[status(thm)],[4278])).
% 0.82/1.03 tff(4280,plain,
% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(z, s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.03 inference(transitivity,[status(thm)],[4279, 4277])).
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% 0.82/1.03 inference(quant_inst,[status(thm)],[])).
% 0.82/1.03 tff(4282,plain,
% 0.82/1.03 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, elem!1)) | (~b(z, s(s(s(z))))) | (~b(s(s(s(z))), elem!1))),
% 0.82/1.03 inference(modus_ponens,[status(thm)],[4281, 4280])).
% 0.82/1.03 tff(4283,plain,
% 0.82/1.03 (~b(z, s(s(s(z))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4282, 272, 262, 4276])).
% 0.82/1.03 tff(4284,plain,
% 0.82/1.03 (r(z, s(s(s(z))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[1541, 4283])).
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% 0.82/1.03 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4286,plain,
% 0.82/1.03 (((~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), s(s(s(z)))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(z)), s(s(s(z))))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.03 inference(rewrite,[status(thm)],[])).
% 0.82/1.03 tff(4287,plain,
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% 0.82/1.03 inference(monotonicity,[status(thm)],[4286])).
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% 0.82/1.03 inference(transitivity,[status(thm)],[4287, 4285])).
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% 0.82/1.03 inference(modus_ponens,[status(thm)],[4289, 4288])).
% 0.82/1.03 tff(4291,plain,
% 0.82/1.03 (~b(s(s(z)), s(s(s(z))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4290, 272, 326, 4276])).
% 0.82/1.03 tff(4292,plain,
% 0.82/1.03 (r(s(s(z)), s(s(s(z))))),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[3288, 4291])).
% 0.82/1.03 tff(4293,plain,
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% 0.82/1.03 inference(unit_resolution,[status(thm)],[3800, 4292, 4284, 1133])).
% 0.82/1.03 tff(4294,plain,((~b(s(s(z)), elem!1)) | (~b(z, elem!1)) | b(s(s(s(elem!1))), elem!1) | (~r(elem!1, s(s(s(z))))) | (s(z) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.03 tff(4295,plain,
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% 0.82/1.03 (~b(s(s(s(z))), z)),
% 0.82/1.03 inference(unit_resolution,[status(thm)],[4000, 272, 262, 4112])).
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% 0.82/1.04 tff(4301,plain,
% 0.82/1.04 (r(s(s(s(s(z)))), elem!1)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[4096, 4300, 4297])).
% 0.82/1.04 tff(4302,plain,
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% 0.82/1.04 inference(unit_resolution,[status(thm)],[4076, 4301, 434])).
% 0.82/1.04 tff(4303,plain,
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% 0.82/1.04 inference(unit_resolution,[status(thm)],[143, 4302, 1416])).
% 0.82/1.04 tff(4304,plain,
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% 0.82/1.04 inference(unit_resolution,[status(thm)],[1005, 4303, 1032])).
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% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(4306,plain,
% 0.82/1.04 (((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(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)))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(4307,plain,
% 0.82/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(z), s(s(s(z))))) | (~b(s(s(s(z))), elem!1))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[4306])).
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% 0.82/1.04 inference(modus_ponens,[status(thm)],[4309, 4308])).
% 0.82/1.04 tff(4311,plain,
% 0.82/1.04 (~b(s(z), s(s(s(z))))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[4310, 272, 253, 4112])).
% 0.82/1.04 tff(4312,plain,
% 0.82/1.04 (r(s(z), s(s(s(z))))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3827, 4311])).
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% 0.82/1.04 tff(4314,plain,((~b(s(s(s(z))), elem!1)) | (~r(s(z), z)) | (~b(z, elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.04 tff(4315,plain,
% 0.82/1.04 (~r(s(z), z)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[4314, 4303, 262, 4112])).
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% 0.82/1.04 tff(4317,plain,((~b(s(s(s(z))), elem!1)) | (~b(z, elem!1)) | (~b(elem!1, z)) | (s(z) = elem!1) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.04 tff(4318,plain,
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% 0.82/1.04 tff(4321,plain,
% 0.82/1.04 (b(s(s(z)), s(s(s(z))))),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[3288, 4320])).
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% 0.82/1.04 inference(rewrite,[status(thm)],[])).
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% 0.82/1.04 inference(quant_inst,[status(thm)],[])).
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% 0.82/1.04 inference(modus_ponens,[status(thm)],[4380, 4379])).
% 0.82/1.04 tff(4382,plain,
% 0.82/1.04 (~r(s(s(s(s(z)))), z)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[4381, 371, 443, 4032])).
% 0.82/1.04 tff(4383,plain,
% 0.82/1.04 (b(s(s(s(s(z)))), z)),
% 0.82/1.04 inference(unit_resolution,[status(thm)],[4110, 139, 4107, 4382])).
% 0.82/1.04 tff(4384,plain,
% 0.82/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(4385,plain,
% 0.82/1.04 (((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))) <=> ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.04 inference(rewrite,[status(thm)],[])).
% 0.82/1.04 tff(4386,plain,
% 0.82/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z))))))))),
% 0.82/1.04 inference(monotonicity,[status(thm)],[4385])).
% 0.82/1.04 tff(4387,plain,
% 0.82/1.04 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.04 inference(transitivity,[status(thm)],[4386, 4384])).
% 0.82/1.04 tff(4388,plain,
% 0.82/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(z), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(z), s(s(s(s(z)))))))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4389,plain,
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% 0.82/1.05 inference(modus_ponens,[status(thm)],[4388, 4387])).
% 0.82/1.05 tff(4390,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4389, 272, 1308, 4383, 4050])).
% 0.82/1.05 tff(4391,plain,((~r(s(s(s(s(z)))), elem!1)) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4392,plain,
% 0.82/1.05 (~r(s(s(s(s(z)))), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4391, 4378, 4365, 4364])).
% 0.82/1.05 tff(4393,plain,
% 0.82/1.05 (b(s(s(s(s(z)))), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4096, 4392, 3638])).
% 0.82/1.05 tff(4394,plain,
% 0.82/1.05 (~(elem!1 = s(s(s(z))))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3662, 3606])).
% 0.82/1.05 tff(4395,plain,
% 0.82/1.05 (~(s(s(s(z))) = elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3669, 4394])).
% 0.82/1.05 tff(4396,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4397,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(z))), elem!1)) | (~r(s(s(s(z))), z)))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4398,plain,
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% 0.82/1.05 inference(modus_ponens,[status(thm)],[4397, 4396])).
% 0.82/1.05 tff(4399,plain,
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% 0.82/1.05 inference(unit_resolution,[status(thm)],[4398, 371, 443, 4199])).
% 0.82/1.05 tff(4400,plain,
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% 0.82/1.05 inference(unit_resolution,[status(thm)],[3843, 4399])).
% 0.82/1.05 tff(4401,plain,
% 0.82/1.05 (~r(s(z), s(s(s(z))))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4152, 371, 1101, 4199])).
% 0.82/1.05 tff(4402,plain,
% 0.82/1.05 (b(s(z), s(s(s(z))))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3827, 4401])).
% 0.82/1.05 tff(4403,plain,
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% 0.82/1.05 inference(unit_resolution,[status(thm)],[3838, 4402, 4400, 1308])).
% 0.82/1.05 tff(4404,plain,((~r(s(s(s(z))), elem!1)) | (~b(s(z), z)) | (~r(s(z), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4405,plain,
% 0.82/1.05 (~r(s(s(s(z))), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4404, 4378, 4365, 4364])).
% 0.82/1.05 tff(4406,plain,
% 0.82/1.05 (b(s(s(s(z))), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3993, 4405, 4395])).
% 0.82/1.05 tff(4407,plain,
% 0.82/1.05 ((s(s(s(s(z)))) = s(s(z))) <=> (s(s(z)) = s(s(s(s(z)))))),
% 0.82/1.05 inference(commutativity,[status(thm)],[])).
% 0.82/1.05 tff(4408,plain,
% 0.82/1.05 ((s(s(z)) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(s(z)))),
% 0.82/1.05 inference(symmetry,[status(thm)],[4407])).
% 0.82/1.05 tff(4409,plain,
% 0.82/1.05 ((~(s(s(z)) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(s(z))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4408])).
% 0.82/1.05 tff(4410,plain,
% 0.82/1.05 (~(s(s(s(s(z)))) = s(s(z)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4062, 4409])).
% 0.82/1.05 tff(4411,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4412,plain,
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% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4413,plain,
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% 0.82/1.05 inference(monotonicity,[status(thm)],[4412])).
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% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(s(z)))), s(s(z)))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4413, 4411])).
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% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4416,plain,
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% 0.82/1.05 inference(modus_ponens,[status(thm)],[4415, 4414])).
% 0.82/1.05 tff(4417,plain,
% 0.82/1.05 (~b(s(s(s(s(z)))), s(s(z)))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4416, 272, 326, 4098])).
% 0.82/1.05 tff(4418,plain,
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% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4419,plain,
% 0.82/1.05 ((~![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))))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4420,plain,
% 0.82/1.05 ((~![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)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4419, 4418])).
% 0.82/1.05 tff(4421,plain,
% 0.82/1.05 ((s(s(s(s(z)))) = s(s(z))) | r(s(s(s(s(z)))), s(s(z)))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4420, 139, 4417])).
% 0.82/1.05 tff(4422,plain,
% 0.82/1.05 (r(s(s(s(s(z)))), s(s(z)))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4421, 4410])).
% 0.82/1.05 tff(4423,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4424,plain,
% 0.82/1.05 (((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z))))) <=> ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4425,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4424])).
% 0.82/1.05 tff(4426,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4425, 4423])).
% 0.82/1.05 tff(4427,plain,
% 0.82/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4428,plain,
% 0.82/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), elem!1)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), elem!1))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4427, 4426])).
% 0.82/1.05 tff(4429,plain,
% 0.82/1.05 (~b(s(s(s(z))), s(s(z)))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4428, 272, 326, 4112])).
% 0.82/1.05 tff(4430,plain,
% 0.82/1.05 (r(s(s(s(z))), s(s(z)))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[3950, 4429])).
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% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4432,plain,
% 0.82/1.05 (((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4433,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4432])).
% 0.82/1.05 tff(4434,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4433, 4431])).
% 0.82/1.05 tff(4435,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4436,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(s(z)))) | (~r(s(s(s(s(z)))), s(s(z)))) | (~r(s(s(s(z))), s(s(s(s(z))))))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4435, 4434])).
% 0.82/1.05 tff(4437,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4436, 371, 4430, 4422, 4128])).
% 0.82/1.05 tff(4438,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4439,plain,
% 0.82/1.05 (~b(s(s(z)), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4438, 4406, 4393])).
% 0.82/1.05 tff(4440,plain,
% 0.82/1.05 (r(s(s(z)), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[476, 4439, 3639])).
% 0.82/1.05 tff(4441,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4442,plain,
% 0.82/1.05 (((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z))) <=> ((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4443,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4442])).
% 0.82/1.05 tff(4444,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z))))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4443, 4441])).
% 0.82/1.05 tff(4445,plain,
% 0.82/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(z))) | (~b(s(s(z)), s(z))) | (~b(z, s(z))) | (~b(s(s(z)), z)))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4446,plain,
% 0.82/1.05 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(z, s(z))) | (~b(s(s(z)), s(z)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4445, 4444])).
% 0.82/1.05 tff(4447,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4446, 272, 779, 1333, 3440])).
% 0.82/1.05 tff(4448,plain,((~b(z, s(z))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4449,plain,
% 0.82/1.05 (~b(s(s(z)), s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4448, 983, 1333])).
% 0.82/1.05 tff(4450,plain,
% 0.82/1.05 (r(s(s(z)), s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[359, 4449])).
% 0.82/1.05 tff(4451,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[1111, 371, 434, 1101, 4450])).
% 0.82/1.05 tff(4452,plain,((~r(s(s(z)), elem!1)) | (~r(s(z), elem!1)) | (~b(z, s(z))) | (~r(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4453,plain,
% 0.82/1.05 (~r(elem!1, z)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4452, 4440, 4370, 4365])).
% 0.82/1.05 tff(4454,plain,
% 0.82/1.05 (b(elem!1, z)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[997, 4453, 4368])).
% 0.82/1.05 tff(4455,plain,
% 0.82/1.05 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, elem!1)),
% 0.82/1.05 inference(monotonicity,[status(thm)],[3607])).
% 0.82/1.05 tff(4456,plain,
% 0.82/1.05 (r(z, elem!1) <=> r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.05 inference(symmetry,[status(thm)],[4455])).
% 0.82/1.05 tff(4457,plain,
% 0.82/1.05 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4364, 4456])).
% 0.82/1.05 tff(4458,plain,
% 0.82/1.05 (~(s(s(z)) = elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[219, 3655])).
% 0.82/1.05 tff(4459,plain,
% 0.82/1.05 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, elem!1)),
% 0.82/1.05 inference(monotonicity,[status(thm)],[3655])).
% 0.82/1.05 tff(4460,plain,
% 0.82/1.05 (r(z, elem!1)),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[2290, 4459])).
% 0.82/1.05 tff(4461,plain,
% 0.82/1.05 (elem!1 = s(s(elem!1))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[222, 78])).
% 0.82/1.05 tff(4462,plain,
% 0.82/1.05 (r(z, s(s(elem!1))) <=> r(z, elem!1)),
% 0.82/1.05 inference(monotonicity,[status(thm)],[222])).
% 0.82/1.05 tff(4463,plain,
% 0.82/1.05 (r(z, elem!1) <=> r(z, s(s(elem!1)))),
% 0.82/1.05 inference(symmetry,[status(thm)],[4462])).
% 0.82/1.05 tff(4464,plain,
% 0.82/1.05 (r(z, s(s(s(s(s(s(elem!1))))))) <=> r(z, s(s(elem!1)))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4459, 4463])).
% 0.82/1.05 tff(4465,plain,
% 0.82/1.05 (r(z, s(s(elem!1)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[2290, 4464])).
% 0.82/1.05 tff(4466,assumption,(r(elem!1, s(z))), introduced(assumption)).
% 0.82/1.05 tff(4467,assumption,(r(s(s(z)), s(z))), introduced(assumption)).
% 0.82/1.05 tff(4468,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4469,plain,
% 0.82/1.05 (((~r(elem!1, s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1))) <=> ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4470,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z)))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4469])).
% 0.82/1.05 tff(4471,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~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)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4470, 4468])).
% 0.82/1.05 tff(4472,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~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)))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4473,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), elem!1)) | (~r(s(s(z)), s(z))) | (~r(elem!1, s(z)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4472, 4471])).
% 0.82/1.05 tff(4474,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4473, 371, 434, 4466, 4467])).
% 0.82/1.05 tff(4475,plain,((~r(s(s(z)), s(z))) | (~r(s(s(z)), elem!1)) | (~r(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4476,plain,
% 0.82/1.05 (~r(s(s(z)), s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4475, 4466, 434])).
% 0.82/1.05 tff(4477,plain,
% 0.82/1.05 (b(s(s(z)), s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[359, 4476])).
% 0.82/1.05 tff(4478,plain,
% 0.82/1.05 (~b(z, s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4448, 463, 4477])).
% 0.82/1.05 tff(4479,plain,
% 0.82/1.05 (r(z, s(z))),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[397, 4478])).
% 0.82/1.05 tff(4480,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4481,plain,
% 0.82/1.05 (((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1))) <=> ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.05 tff(4482,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))))),
% 0.82/1.05 inference(monotonicity,[status(thm)],[4481])).
% 0.82/1.05 tff(4483,plain,
% 0.82/1.05 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z))))),
% 0.82/1.05 inference(transitivity,[status(thm)],[4482, 4480])).
% 0.82/1.05 tff(4484,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(z))) | (~r(z, s(z))) | (~r(z, elem!1)))),
% 0.82/1.05 inference(quant_inst,[status(thm)],[])).
% 0.82/1.05 tff(4485,plain,
% 0.82/1.05 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(z, s(z))) | (~r(elem!1, s(z)))),
% 0.82/1.05 inference(modus_ponens,[status(thm)],[4484, 4483])).
% 0.82/1.05 tff(4486,plain,
% 0.82/1.05 ($false),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4485, 371, 443, 4479, 4466])).
% 0.82/1.05 tff(4487,plain,((~r(z, elem!1)) | (~r(elem!1, s(z))) | (~r(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.05 tff(4488,plain,
% 0.82/1.05 (~r(s(s(z)), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[4487, 4466, 443])).
% 0.82/1.05 tff(4489,plain,
% 0.82/1.05 (b(s(s(z)), elem!1)),
% 0.82/1.05 inference(unit_resolution,[status(thm)],[476, 4488, 1346])).
% 0.82/1.05 tff(4490,plain,
% 0.82/1.05 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 0.82/1.05 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(4491,plain,
% 0.82/1.06 (((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z)))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(4492,plain,
% 0.82/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(s(s(z)), z)) | (~b(elem!1, z)) | (~b(s(s(z)), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), elem!1)) | (~b(elem!1, z))))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[4491])).
% 0.82/1.06 tff(4493,plain,
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% 0.82/1.06 inference(transitivity,[status(thm)],[4547, 4545])).
% 0.82/1.06 tff(4549,plain,
% 0.82/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(z)))))),
% 0.82/1.06 inference(quant_inst,[status(thm)],[])).
% 0.82/1.06 tff(4550,plain,
% 0.82/1.06 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), s(s(z)))) | (~b(s(s(z)), s(s(elem!1)))) | (~b(s(z), s(s(elem!1))))),
% 0.82/1.06 inference(modus_ponens,[status(thm)],[4549, 4548])).
% 0.82/1.06 tff(4551,plain,
% 0.82/1.06 (~b(s(z), s(s(z)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4550, 272, 2059, 4544])).
% 0.82/1.06 tff(4552,plain,
% 0.82/1.06 (~b(s(s(z)), z)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4497, 326, 1032])).
% 0.82/1.06 tff(4553,plain,
% 0.82/1.06 (r(s(s(z)), z)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[462, 4552])).
% 0.82/1.06 tff(4554,plain,
% 0.82/1.06 (~r(s(z), s(s(z)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[808, 371, 4553, 672])).
% 0.82/1.06 tff(4555,plain,
% 0.82/1.06 ($false),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[804, 4554, 4551])).
% 0.82/1.06 tff(4556,plain,((~b(s(s(z)), elem!1)) | (~r(s(z), z)) | (~b(s(z), s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.06 tff(4557,plain,
% 0.82/1.06 (~r(s(z), z)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4556, 1032, 64, 2059, 326])).
% 0.82/1.06 tff(4558,plain,
% 0.82/1.06 ($false),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[289, 4557, 4542])).
% 0.82/1.06 tff(4559,plain,((~b(elem!1, z)) | (~(elem!1 = s(s(elem!1)))) | (~b(s(z), s(s(elem!1)))) | (~b(s(s(z)), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.06 tff(4560,plain,
% 0.82/1.06 (~b(s(z), s(s(elem!1)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4559, 4539, 64, 1032, 4489])).
% 0.82/1.06 tff(4561,plain,
% 0.82/1.06 (r(s(z), s(s(elem!1)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[862, 4560])).
% 0.82/1.06 tff(4562,plain,
% 0.82/1.06 ($false),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1016, 4561, 4541, 1008])).
% 0.82/1.06 tff(4563,plain,((~r(elem!1, s(z))) | (~r(z, s(s(elem!1)))) | (~(elem!1 = s(s(elem!1)))) | (~b(elem!1, z)) | (s(z) = elem!1) | (~r(z, elem!1)) | (elem!1 = s(s(s(z)))) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.06 tff(4564,plain,
% 0.82/1.06 (~r(elem!1, s(z))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4563, 4465, 4461, 1032, 3658, 4460, 4089, 4458])).
% 0.82/1.06 tff(4565,plain,
% 0.82/1.06 ((~(s(z) = elem!1)) <=> (~(elem!1 = s(z)))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[1863])).
% 0.82/1.06 tff(4566,plain,
% 0.82/1.06 (~(elem!1 = s(z))),
% 0.82/1.06 inference(modus_ponens,[status(thm)],[3658, 4565])).
% 0.82/1.06 tff(4567,plain,
% 0.82/1.06 (((~![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)))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(4568,plain,
% 0.82/1.06 ((~![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)))),
% 0.82/1.06 inference(quant_inst,[status(thm)],[])).
% 0.82/1.06 tff(4569,plain,
% 0.82/1.06 ((~![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))),
% 0.82/1.06 inference(modus_ponens,[status(thm)],[4568, 4567])).
% 0.82/1.06 tff(4570,plain,
% 0.82/1.06 (b(elem!1, s(z))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4569, 139, 4566, 4564])).
% 0.82/1.06 tff(4571,plain,
% 0.82/1.06 (~(s(elem!1) = s(z))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[50, 3657])).
% 0.82/1.06 tff(4572,plain,
% 0.82/1.06 (r(s(elem!1), s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[3620])).
% 0.82/1.06 tff(4573,plain,
% 0.82/1.06 (r(s(s(s(elem!1))), s(z)) <=> r(s(elem!1), s(z))),
% 0.82/1.06 inference(symmetry,[status(thm)],[4572])).
% 0.82/1.06 tff(4574,plain,
% 0.82/1.06 (elem!1 = s(s(s(elem!1)))),
% 0.82/1.06 inference(transitivity,[status(thm)],[4087, 3620])).
% 0.82/1.06 tff(4575,plain,
% 0.82/1.06 (r(elem!1, s(z)) <=> r(s(s(s(elem!1))), s(z))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[4574])).
% 0.82/1.06 tff(4576,plain,
% 0.82/1.06 (r(elem!1, s(z)) <=> r(s(elem!1), s(z))),
% 0.82/1.06 inference(transitivity,[status(thm)],[4575, 4573])).
% 0.82/1.06 tff(4577,plain,
% 0.82/1.06 ((~r(elem!1, s(z))) <=> (~r(s(elem!1), s(z)))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[4576])).
% 0.82/1.06 tff(4578,plain,
% 0.82/1.06 (~r(s(elem!1), s(z))),
% 0.82/1.06 inference(modus_ponens,[status(thm)],[4564, 4577])).
% 0.82/1.06 tff(4579,plain,
% 0.82/1.06 (b(s(elem!1), s(z))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[324, 4578, 4571])).
% 0.82/1.06 tff(4580,plain,
% 0.82/1.06 (~b(s(z), z)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1316, 4579, 399])).
% 0.82/1.06 tff(4581,plain,
% 0.82/1.06 (r(s(z), z)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[289, 4580])).
% 0.82/1.06 tff(4582,plain,
% 0.82/1.06 (~b(s(z), s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[3919, 3781, 3911])).
% 0.82/1.06 tff(4583,plain,
% 0.82/1.06 (r(s(z), s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[3827, 4582])).
% 0.82/1.06 tff(4584,plain,
% 0.82/1.06 (~b(z, s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4515, 3781, 1032])).
% 0.82/1.06 tff(4585,plain,
% 0.82/1.06 (r(z, s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1541, 4584])).
% 0.82/1.06 tff(4586,plain,
% 0.82/1.06 (((~![X0: $i, X2: $i, X1: $i] : ((~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))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(4587,plain,
% 0.82/1.06 (((~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))))))),
% 0.82/1.06 inference(rewrite,[status(thm)],[])).
% 0.82/1.06 tff(4588,plain,
% 0.82/1.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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)))))))),
% 0.82/1.06 inference(monotonicity,[status(thm)],[4587])).
% 0.82/1.06 tff(4589,plain,
% 0.82/1.06 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~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))))))),
% 0.82/1.06 inference(transitivity,[status(thm)],[4588, 4586])).
% 0.82/1.06 tff(4590,plain,
% 0.82/1.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), z)))),
% 0.82/1.06 inference(quant_inst,[status(thm)],[])).
% 0.82/1.06 tff(4591,plain,
% 0.82/1.06 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), z)) | (~r(z, s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.82/1.06 inference(modus_ponens,[status(thm)],[4590, 4589])).
% 0.82/1.06 tff(4592,plain,
% 0.82/1.06 ($false),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4591, 371, 672, 4585, 4583])).
% 0.82/1.06 tff(4593,plain,((~b(elem!1, s(s(s(z))))) | (~r(s(z), z)) | (~b(elem!1, z)) | (~b(elem!1, s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.06 tff(4594,plain,
% 0.82/1.06 (~b(elem!1, s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4593, 4581, 1032, 4570])).
% 0.82/1.06 tff(4595,plain,
% 0.82/1.06 (r(elem!1, s(s(s(z))))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1856, 4594, 4089])).
% 0.82/1.06 tff(4596,plain,
% 0.82/1.06 (~(elem!1 = s(s(z)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[3956, 4458])).
% 0.82/1.06 tff(4597,plain,
% 0.82/1.06 (~r(s(z), s(s(elem!1)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1016, 4581, 4465])).
% 0.82/1.06 tff(4598,plain,
% 0.82/1.06 (b(s(z), s(s(elem!1)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[862, 4597])).
% 0.82/1.06 tff(4599,plain,
% 0.82/1.06 (~b(s(s(z)), elem!1)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[4556, 4598, 4461, 1032, 4581])).
% 0.82/1.06 tff(4600,plain,
% 0.82/1.06 (r(s(s(z)), elem!1)),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[476, 4599, 4458])).
% 0.82/1.06 tff(4601,plain,
% 0.82/1.06 (~r(z, s(s(z)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1063, 4600, 4460])).
% 0.82/1.06 tff(4602,plain,
% 0.82/1.06 (b(z, s(s(z)))),
% 0.82/1.06 inference(unit_resolution,[status(thm)],[1073, 4601])).
% 0.82/1.06 tff(4603,assumption,(b(elem!1, s(s(z)))), introduced(assumption)).
% 0.82/1.06 tff(4604,plain,
% 0.82/1.06 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4605,plain,
% 0.82/1.07 (((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z))) <=> ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4606,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z))))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4605])).
% 0.82/1.07 tff(4607,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))))),
% 0.82/1.07 inference(transitivity,[status(thm)],[4606, 4604])).
% 0.82/1.07 tff(4608,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z)))) | (~b(elem!1, z)))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4609,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, z)) | (~b(elem!1, s(s(z)))) | (~b(z, s(s(z))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4608, 4607])).
% 0.82/1.07 tff(4610,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4609, 272, 1032, 1371, 4603])).
% 0.82/1.07 tff(4611,plain,((~b(elem!1, s(s(z)))) | (~b(elem!1, z)) | (~b(z, s(s(z))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4612,plain,
% 0.82/1.07 (~b(elem!1, s(s(z)))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4611, 4602, 1032])).
% 0.82/1.07 tff(4613,plain,
% 0.82/1.07 (r(elem!1, s(s(z)))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[3984, 4612, 4596])).
% 0.82/1.07 tff(4614,assumption,(r(elem!1, s(s(z)))), introduced(assumption)).
% 0.82/1.07 tff(4615,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4616,plain,
% 0.82/1.07 (((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z))))) <=> ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4617,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z)))))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4616])).
% 0.82/1.07 tff(4618,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(elem!1, s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))))),
% 0.82/1.07 inference(transitivity,[status(thm)],[4617, 4615])).
% 0.82/1.07 tff(4619,plain,
% 0.82/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(s(z))))) | (~r(elem!1, s(s(z)))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4620,plain,
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% 0.82/1.07 inference(modus_ponens,[status(thm)],[4619, 4618])).
% 0.82/1.07 tff(4621,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4620, 371, 4614, 1472, 3792])).
% 0.82/1.07 tff(4622,plain,((~r(s(s(z)), s(s(s(z))))) | (~r(elem!1, s(s(z)))) | (~r(elem!1, s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4623,plain,
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% 0.82/1.07 inference(unit_resolution,[status(thm)],[4622, 4613, 4595])).
% 0.82/1.07 tff(4624,plain,
% 0.82/1.07 (b(s(s(z)), s(s(s(z))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[3288, 4623])).
% 0.82/1.07 tff(4625,plain,
% 0.82/1.07 (~r(z, s(s(s(z))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[1529, 4595, 4460])).
% 0.82/1.07 tff(4626,plain,
% 0.82/1.07 (b(z, s(s(s(z))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[1541, 4625])).
% 0.82/1.07 tff(4627,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4628,plain,
% 0.82/1.07 (((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z))))) <=> ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4629,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z))))) | (~b(z, s(s(z)))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4628])).
% 0.82/1.07 tff(4630,plain,
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% 0.82/1.07 inference(transitivity,[status(thm)],[4629, 4627])).
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% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4632,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(z, s(s(z)))) | (~b(z, s(s(s(z))))) | (~b(s(s(z)), s(s(s(z)))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4631, 4630])).
% 0.82/1.07 tff(4633,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4632, 272, 4602, 4626, 4624])).
% 0.82/1.07 tff(4634,plain,((~r(z, s(s(s(s(s(s(elem!1)))))))) | (~b(elem!1, z)) | (~b(s(elem!1), z)) | (~(s(s(elem!1)) = elem!1)) | (~(s(elem!1) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4635,plain,
% 0.82/1.07 (~b(s(elem!1), z)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4634, 4454, 4457, 3606, 4367])).
% 0.82/1.07 tff(4636,plain,
% 0.82/1.07 (b(s(elem!1), z)),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[1032, 1874])).
% 0.82/1.07 tff(4637,assumption,(~b(s(elem!1), z)), introduced(assumption)).
% 0.82/1.07 tff(4638,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4637, 4636])).
% 0.82/1.07 tff(4639,plain,((~(s(elem!1) = elem!1)) | b(s(elem!1), z) | (~b(elem!1, z))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4640,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4639, 4635, 4454, 4367])).
% 0.82/1.07 tff(4641,plain,(b(s(z), elem!1) | b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4642,plain,
% 0.82/1.07 (b(s(z), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4641, 52])).
% 0.82/1.07 tff(4643,assumption,(~(s(s(s(z))) = elem!1)), introduced(assumption)).
% 0.82/1.07 tff(4644,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4645,plain,
% 0.82/1.07 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z))))))) <=> ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4646,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4645])).
% 0.82/1.07 tff(4647,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z)))),
% 0.82/1.07 inference(transitivity,[status(thm)],[4646, 4644])).
% 0.82/1.07 tff(4648,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(z)), s(s(s(s(z)))))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4649,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(z)), z)) | (~b(s(s(z)), s(s(s(s(z)))))) | (~b(s(s(s(s(z)))), z))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4648, 4647])).
% 0.82/1.07 tff(4650,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4649, 272, 463, 4383, 4066])).
% 0.82/1.07 tff(4651,plain,((~r(s(s(z)), elem!1)) | (~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4652,plain,
% 0.82/1.07 (~r(s(s(z)), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4651, 4032, 443])).
% 0.82/1.07 tff(4653,plain,
% 0.82/1.07 (b(s(s(z)), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[476, 4652, 1346])).
% 0.82/1.07 tff(4654,plain,
% 0.82/1.07 (~b(s(z), s(s(z)))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[798, 326, 253])).
% 0.82/1.07 tff(4655,plain,
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% 0.82/1.07 inference(unit_resolution,[status(thm)],[804, 4654])).
% 0.82/1.07 tff(4656,plain,
% 0.82/1.07 (~b(s(s(z)), s(s(s(z))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4290, 272, 326, 4112])).
% 0.82/1.07 tff(4657,plain,
% 0.82/1.07 (r(s(s(z)), s(s(s(z))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[3288, 4656])).
% 0.82/1.07 tff(4658,assumption,(r(s(z), s(s(z)))), introduced(assumption)).
% 0.82/1.07 tff(4659,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4660,plain,
% 0.82/1.07 (((~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(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4661,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4660])).
% 0.82/1.07 tff(4662,plain,
% 0.82/1.07 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))))),
% 0.82/1.07 inference(transitivity,[status(thm)],[4661, 4659])).
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% 0.82/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4664,plain,
% 0.82/1.07 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z))))) | (~r(s(z), s(s(s(z)))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4663, 4662])).
% 0.82/1.07 tff(4665,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4664, 371, 4658, 3792, 3813])).
% 0.82/1.07 tff(4666,plain,((~r(s(z), s(s(s(z))))) | (~r(s(z), s(s(z)))) | (~r(s(s(z)), s(s(s(z)))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4667,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4666, 4312, 4657, 4655])).
% 0.82/1.07 tff(4668,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(z)), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4669,plain,
% 0.82/1.07 (~b(s(s(s(z))), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4668, 4653, 253])).
% 0.82/1.07 tff(4670,plain,
% 0.82/1.07 (r(s(s(s(z))), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[3993, 4669, 4643])).
% 0.82/1.07 tff(4671,plain,
% 0.82/1.07 (~r(s(s(s(z))), s(s(s(s(z)))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4242, 371, 4670, 4032])).
% 0.82/1.07 tff(4672,plain,
% 0.82/1.07 (b(s(s(s(z))), s(s(s(s(z)))))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4127, 139, 4124, 4671])).
% 0.82/1.07 tff(4673,plain,
% 0.82/1.07 (~r(s(s(s(z))), z)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4398, 371, 443, 4670])).
% 0.82/1.07 tff(4674,plain,
% 0.82/1.07 (b(s(s(s(z))), z)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[3843, 4673])).
% 0.82/1.07 tff(4675,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4676,plain,
% 0.82/1.07 (((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))) <=> ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4677,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4676])).
% 0.82/1.07 tff(4678,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.07 inference(transitivity,[status(thm)],[4677, 4675])).
% 0.82/1.07 tff(4679,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4680,plain,
% 0.82/1.07 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(z))), z)) | (~b(s(s(s(s(z)))), z)) | (~b(s(s(s(z))), s(s(s(s(z))))))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4679, 4678])).
% 0.82/1.07 tff(4681,plain,
% 0.82/1.07 ($false),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4680, 272, 4674, 4383, 4672])).
% 0.82/1.07 tff(4682,plain,((~r(s(s(s(s(z)))), elem!1)) | (~r(z, elem!1)) | (s(s(s(z))) = elem!1) | (~b(s(z), elem!1)) | (s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.07 tff(4683,plain,
% 0.82/1.07 (~r(s(s(s(s(z)))), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4682, 4364, 4395, 4642, 3639])).
% 0.82/1.07 tff(4684,plain,
% 0.82/1.07 (b(s(s(s(s(z)))), elem!1)),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4096, 4683, 3638])).
% 0.82/1.07 tff(4685,plain,
% 0.82/1.07 ((s(s(s(s(z)))) = s(z)) <=> (s(z) = s(s(s(s(z)))))),
% 0.82/1.07 inference(commutativity,[status(thm)],[])).
% 0.82/1.07 tff(4686,plain,
% 0.82/1.07 ((s(z) = s(s(s(s(z))))) <=> (s(s(s(s(z)))) = s(z))),
% 0.82/1.07 inference(symmetry,[status(thm)],[4685])).
% 0.82/1.07 tff(4687,plain,
% 0.82/1.07 ((~(s(z) = s(s(s(s(z)))))) <=> (~(s(s(s(s(z)))) = s(z)))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4686])).
% 0.82/1.07 tff(4688,plain,
% 0.82/1.07 (~(s(s(s(s(z)))) = s(z))),
% 0.82/1.07 inference(modus_ponens,[status(thm)],[4046, 4687])).
% 0.82/1.07 tff(4689,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4690,plain,
% 0.82/1.07 (((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z)))) <=> ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1)))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4691,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(s(z)))), s(z))) | (~b(s(s(s(s(z)))), elem!1))))),
% 0.82/1.07 inference(monotonicity,[status(thm)],[4690])).
% 0.82/1.07 tff(4692,plain,
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% 0.82/1.07 inference(transitivity,[status(thm)],[4691, 4689])).
% 0.82/1.07 tff(4693,plain,
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% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4694,plain,
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% 0.82/1.07 inference(modus_ponens,[status(thm)],[4693, 4692])).
% 0.82/1.07 tff(4695,plain,
% 0.82/1.07 (~b(s(s(s(s(z)))), s(z))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4694, 272, 253, 4098])).
% 0.82/1.07 tff(4696,plain,
% 0.82/1.07 (((~![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)))),
% 0.82/1.07 inference(rewrite,[status(thm)],[])).
% 0.82/1.07 tff(4697,plain,
% 0.82/1.07 ((~![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)))),
% 0.82/1.07 inference(quant_inst,[status(thm)],[])).
% 0.82/1.07 tff(4698,plain,
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% 0.82/1.07 inference(modus_ponens,[status(thm)],[4697, 4696])).
% 0.82/1.07 tff(4699,plain,
% 0.82/1.07 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4698, 139, 4695])).
% 0.82/1.07 tff(4700,plain,
% 0.82/1.07 (r(s(s(s(s(z)))), s(z))),
% 0.82/1.07 inference(unit_resolution,[status(thm)],[4699, 4688])).
% 0.82/1.07 tff(4701,plain,
% 0.82/1.07 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~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(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4702,plain,
% 0.82/1.08 (((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(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)))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4703,plain,
% 0.82/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4702])).
% 0.82/1.08 tff(4704,plain,
% 0.82/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(z), elem!1)) | (~b(s(s(s(z))), elem!1)) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(z), elem!1)) | (~b(s(s(s(z))), s(z))) | (~b(s(s(s(z))), elem!1)))),
% 0.82/1.08 inference(transitivity,[status(thm)],[4703, 4701])).
% 0.82/1.08 tff(4705,plain,
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% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
% 0.82/1.08 tff(4706,plain,
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% 0.82/1.08 inference(modus_ponens,[status(thm)],[4705, 4704])).
% 0.82/1.08 tff(4707,plain,
% 0.82/1.08 (~b(s(s(s(z))), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4706, 272, 253, 4112])).
% 0.82/1.08 tff(4708,plain,
% 0.82/1.08 (r(s(s(s(z))), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4257, 4707])).
% 0.82/1.08 tff(4709,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4710,plain,
% 0.82/1.08 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z))))))) <=> ((~r(s(s(s(z))), s(z))) | (~r(s(s(s(s(z)))), s(z))) | (~r(s(s(s(z))), s(s(s(s(z)))))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4711,plain,
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% 0.82/1.08 inference(monotonicity,[status(thm)],[4710])).
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% 0.82/1.08 inference(transitivity,[status(thm)],[4711, 4709])).
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% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
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% 0.82/1.08 inference(modus_ponens,[status(thm)],[4713, 4712])).
% 0.82/1.08 tff(4715,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4714, 371, 4708, 4700, 4128])).
% 0.82/1.08 tff(4716,plain,((~b(s(s(s(z))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(z), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4717,plain,
% 0.82/1.08 (~b(s(s(s(z))), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4716, 4684, 4642])).
% 0.82/1.08 tff(4718,plain,
% 0.82/1.08 (r(s(s(s(z))), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3993, 4717, 4395])).
% 0.82/1.08 tff(4719,assumption,(b(s(s(s(z))), s(s(z)))), introduced(assumption)).
% 0.82/1.08 tff(4720,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3940, 272, 779, 4719, 3829])).
% 0.82/1.08 tff(4721,plain,((~b(s(s(z)), z)) | (~b(s(s(s(z))), s(s(z)))) | (~b(s(s(s(z))), z))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4722,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4721, 4326, 4400, 463])).
% 0.82/1.08 tff(4723,plain,((~r(s(s(s(z))), elem!1)) | (~r(s(s(z)), elem!1)) | (~r(z, elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4724,plain,
% 0.82/1.08 (~r(s(s(z)), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4723, 4718, 4364])).
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% 0.82/1.08 inference(unit_resolution,[status(thm)],[476, 4724, 3639])).
% 0.82/1.08 tff(4726,plain,
% 0.82/1.08 (~b(s(s(z)), s(s(s(s(z)))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4183, 272, 4725, 4684])).
% 0.82/1.08 tff(4727,plain,
% 0.82/1.08 (r(s(s(z)), s(s(s(s(z)))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4065, 139, 4062, 4726])).
% 0.82/1.08 tff(4728,plain,
% 0.82/1.08 (~b(s(s(s(s(z)))), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4694, 272, 4642, 4684])).
% 0.82/1.08 tff(4729,plain,
% 0.82/1.08 ((s(s(s(s(z)))) = s(z)) | r(s(s(s(s(z)))), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4698, 139, 4728])).
% 0.82/1.08 tff(4730,plain,
% 0.82/1.08 (r(s(s(s(s(z)))), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4729, 4688])).
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% 0.82/1.08 (~b(s(s(z)), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[343, 272, 4725, 4642])).
% 0.82/1.08 tff(4732,plain,
% 0.82/1.08 (r(s(s(z)), s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[359, 4731])).
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% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4734,plain,
% 0.82/1.08 (((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z))))))) <=> ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4735,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4734])).
% 0.82/1.08 tff(4736,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z))))),
% 0.82/1.08 inference(transitivity,[status(thm)],[4735, 4733])).
% 0.82/1.08 tff(4737,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(z)))), s(z))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))))),
% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
% 0.82/1.08 tff(4738,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(z)), s(z))) | (~r(s(s(z)), s(s(s(s(z)))))) | (~r(s(s(s(s(z)))), s(z)))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[4737, 4736])).
% 0.82/1.08 tff(4739,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4738, 371, 4732, 4730, 4727])).
% 0.82/1.08 tff(4740,plain,(b(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4741,plain,
% 0.82/1.08 ((~(z = elem!1)) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3108, 4740])).
% 0.82/1.08 tff(4742,plain,
% 0.82/1.08 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4741, 51, 1])).
% 0.82/1.08 tff(4743,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[2232, 51])).
% 0.82/1.08 tff(4744,plain,
% 0.82/1.08 (~(s(s(elem!1)) = elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3624, 4743, 4742])).
% 0.82/1.08 tff(4745,plain,
% 0.82/1.08 (s(elem!1) = s(s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3605, 4744])).
% 0.82/1.08 tff(4746,plain,
% 0.82/1.08 (s(z) = elem!1),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1418, 4745])).
% 0.82/1.08 tff(4747,plain,
% 0.82/1.08 (elem!1 = z),
% 0.82/1.08 inference(symmetry,[status(thm)],[1])).
% 0.82/1.08 tff(4748,plain,
% 0.82/1.08 (s(elem!1) = s(z)),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4747])).
% 0.82/1.08 tff(4749,plain,
% 0.82/1.08 (s(s(z)) = s(elem!1)),
% 0.82/1.08 inference(symmetry,[status(thm)],[4745])).
% 0.82/1.08 tff(4750,plain,
% 0.82/1.08 (s(s(z)) = elem!1),
% 0.82/1.08 inference(transitivity,[status(thm)],[4749, 4748, 4746])).
% 0.82/1.08 tff(4751,plain,
% 0.82/1.08 (s(s(z)) = s(s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1422, 204])).
% 0.82/1.08 tff(4752,plain,
% 0.82/1.08 (s(elem!1) = s(z)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[2391, 4751])).
% 0.82/1.08 tff(4753,plain,
% 0.82/1.08 ((~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))) <=> (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[174])).
% 0.82/1.08 tff(4754,plain,
% 0.82/1.08 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[662, 4753])).
% 0.82/1.08 tff(4755,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[28, 4754])).
% 0.82/1.08 tff(4756,plain,((s(s(s(s(s(s(elem!1)))))) = s(s(elem!1))) | (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4757,plain,
% 0.82/1.08 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4756, 967])).
% 0.82/1.08 tff(4758,plain,
% 0.82/1.08 (~(z = elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4741, 4757, 220])).
% 0.82/1.08 tff(4759,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1886, 4758, 4752])).
% 0.82/1.08 tff(4760,plain,(~(s(s(z)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4761,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4760, 4750])).
% 0.82/1.08 tff(4762,plain,(~(z = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4763,plain,
% 0.82/1.08 (s(elem!1) = s(s(z))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[3605, 233])).
% 0.82/1.08 tff(4764,plain,
% 0.82/1.08 (s(z) = elem!1),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1418, 4763])).
% 0.82/1.08 tff(4765,plain,
% 0.82/1.08 ((s(s(s(s(s(s(s(elem!1))))))) = s(z)) <=> (s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.08 tff(4766,plain,
% 0.82/1.08 ((~(s(s(s(s(s(s(s(elem!1))))))) = s(z))) <=> (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4765])).
% 0.82/1.08 tff(4767,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(s(elem!1))))))) = elem!1)),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[1643, 4766])).
% 0.82/1.08 tff(4768,plain,
% 0.82/1.08 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (elem!1 = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.08 tff(4769,plain,
% 0.82/1.08 ((s(z) = s(s(s(s(s(s(elem!1))))))) <=> (s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.82/1.08 inference(transitivity,[status(thm)],[4768, 127])).
% 0.82/1.08 tff(4770,plain,
% 0.82/1.08 ((~(s(z) = s(s(s(s(s(s(elem!1)))))))) <=> (~(s(s(s(s(s(s(elem!1)))))) = elem!1))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4769])).
% 0.82/1.08 tff(4771,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(elem!1)))))) = elem!1)),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[155, 4770])).
% 0.82/1.08 tff(4772,plain,
% 0.82/1.08 (~(s(elem!1) = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1433, 4764])).
% 0.82/1.08 tff(4773,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(elem!1)))))) = s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[502, 4772])).
% 0.82/1.08 tff(4774,plain,
% 0.82/1.08 (s(s(z)) = s(elem!1)),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.08 tff(4775,plain,
% 0.82/1.08 (r(z, s(s(z))) <=> r(z, s(elem!1))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4774])).
% 0.82/1.08 tff(4776,plain,
% 0.82/1.08 (b(z, s(s(z))) <=> b(z, s(elem!1))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4774])).
% 0.82/1.08 tff(4777,plain,
% 0.82/1.08 (b(z, s(elem!1)) <=> b(z, s(s(z)))),
% 0.82/1.08 inference(symmetry,[status(thm)],[4776])).
% 0.82/1.08 tff(4778,plain,
% 0.82/1.08 ((~b(z, s(elem!1))) <=> (~b(z, s(s(z))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4777])).
% 0.82/1.08 tff(4779,plain,
% 0.82/1.08 (~b(z, s(s(z)))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[1247, 4778])).
% 0.82/1.08 tff(4780,plain,
% 0.82/1.08 (r(z, s(s(z)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1073, 4779])).
% 0.82/1.08 tff(4781,plain,
% 0.82/1.08 (r(z, s(elem!1))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[4780, 4775])).
% 0.82/1.08 tff(4782,plain,
% 0.82/1.08 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1713, 272, 262, 504])).
% 0.82/1.08 tff(4783,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4784,plain,
% 0.82/1.08 (((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4785,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4784])).
% 0.82/1.08 tff(4786,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.08 inference(transitivity,[status(thm)],[4785, 4783])).
% 0.82/1.08 tff(4787,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
% 0.82/1.08 tff(4788,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(z, s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[4787, 4786])).
% 0.82/1.08 tff(4789,plain,
% 0.82/1.08 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4788, 371, 528, 2162])).
% 0.82/1.08 tff(4790,plain,
% 0.82/1.08 ($false),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1723, 4789, 4782])).
% 0.82/1.08 tff(4791,plain,((~b(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(elem!1))) | (~b(z, elem!1)) | (s(s(s(s(s(s(elem!1)))))) = s(elem!1)) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.08 tff(4792,plain,
% 0.82/1.08 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4791, 4781, 262, 4773, 291])).
% 0.82/1.08 tff(4793,plain,
% 0.82/1.08 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[545, 4792, 4771])).
% 0.82/1.08 tff(4794,plain,
% 0.82/1.08 (~(s(s(elem!1)) = s(s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1443, 4772])).
% 0.82/1.08 tff(4795,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(s(elem!1))))))) = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1460, 4794])).
% 0.82/1.08 tff(4796,plain,
% 0.82/1.08 (~b(s(s(elem!1)), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1234, 262, 291, 2372])).
% 0.82/1.08 tff(4797,plain,
% 0.82/1.08 (r(s(s(elem!1)), elem!1)),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[843, 4796, 233])).
% 0.82/1.08 tff(4798,plain,
% 0.82/1.08 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[2682, 371, 4797, 4793])).
% 0.82/1.08 tff(4799,plain,
% 0.82/1.08 (~(s(s(elem!1)) = s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[172, 4764])).
% 0.82/1.08 tff(4800,plain,
% 0.82/1.08 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[963, 139, 4799, 4798])).
% 0.82/1.08 tff(4801,plain,
% 0.82/1.08 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[549, 371, 4797, 4793])).
% 0.82/1.08 tff(4802,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(elem!1)))))) = s(s(elem!1)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[179, 4799])).
% 0.82/1.08 tff(4803,plain,
% 0.82/1.08 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[611, 139, 4802, 4801])).
% 0.82/1.08 tff(4804,plain,
% 0.82/1.08 (~(s(s(s(s(s(s(s(elem!1))))))) = s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1657, 4771])).
% 0.82/1.08 tff(4805,plain,
% 0.82/1.08 (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1739, 371, 415, 1768])).
% 0.82/1.08 tff(4806,plain,
% 0.82/1.08 (b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[527, 4805, 1736])).
% 0.82/1.08 tff(4807,plain,
% 0.82/1.08 (~b(s(s(elem!1)), s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[1618, 4806, 551])).
% 0.82/1.08 tff(4808,plain,
% 0.82/1.08 (r(s(s(elem!1)), s(elem!1))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[660, 4807, 244])).
% 0.82/1.08 tff(4809,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4810,plain,
% 0.82/1.08 (((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1))))) <=> ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4811,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))))),
% 0.82/1.08 inference(monotonicity,[status(thm)],[4810])).
% 0.82/1.08 tff(4812,plain,
% 0.82/1.08 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.82/1.08 inference(transitivity,[status(thm)],[4811, 4809])).
% 0.82/1.08 tff(4813,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(elem!1))) | (~r(z, s(s(elem!1)))))),
% 0.82/1.08 inference(quant_inst,[status(thm)],[])).
% 0.82/1.08 tff(4814,plain,
% 0.82/1.08 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(z, s(s(elem!1))))),
% 0.82/1.08 inference(modus_ponens,[status(thm)],[4813, 4812])).
% 0.82/1.08 tff(4815,plain,
% 0.82/1.08 (~r(z, s(s(elem!1)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[4814, 371, 4808, 2162])).
% 0.82/1.08 tff(4816,plain,
% 0.82/1.08 (b(z, s(s(elem!1)))),
% 0.82/1.08 inference(unit_resolution,[status(thm)],[579, 4815])).
% 0.82/1.08 tff(4817,plain,
% 0.82/1.08 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.08 inference(rewrite,[status(thm)],[])).
% 0.82/1.08 tff(4818,plain,
% 0.82/1.08 (((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4819,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4818])).
% 0.82/1.09 tff(4820,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(transitivity,[status(thm)],[4819, 4817])).
% 0.82/1.09 tff(4821,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(quant_inst,[status(thm)],[])).
% 0.82/1.09 tff(4822,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(z, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(z, s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.09 inference(modus_ponens,[status(thm)],[4821, 4820])).
% 0.82/1.09 tff(4823,plain,
% 0.82/1.09 (~b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4822, 272, 4816, 4806, 551])).
% 0.82/1.09 tff(4824,plain,
% 0.82/1.09 (r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1723, 4823])).
% 0.82/1.09 tff(4825,plain,
% 0.82/1.09 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[2293, 4824, 262, 1652, 552])).
% 0.82/1.09 tff(4826,plain,
% 0.82/1.09 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1706, 4825, 1648])).
% 0.82/1.09 tff(4827,plain,
% 0.82/1.09 (~r(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1666, 371, 415, 1768])).
% 0.82/1.09 tff(4828,plain,
% 0.82/1.09 (b(s(elem!1), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[695, 4827, 500])).
% 0.82/1.09 tff(4829,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4830,plain,
% 0.82/1.09 (((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))) <=> ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4831,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4830])).
% 0.82/1.09 tff(4832,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(elem!1), s(s(s(s(s(s(elem!1)))))))) | (~b(s(elem!1), elem!1)) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))) | (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(transitivity,[status(thm)],[4831, 4829])).
% 0.82/1.09 tff(4833,plain,
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% 0.82/1.09 inference(quant_inst,[status(thm)],[])).
% 0.82/1.09 tff(4834,plain,
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% 0.82/1.09 inference(modus_ponens,[status(thm)],[4833, 4832])).
% 0.82/1.09 tff(4835,plain,
% 0.82/1.09 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4834, 272, 291, 4828, 4826])).
% 0.82/1.09 tff(4836,plain,
% 0.82/1.09 (r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1699, 139, 1696, 4835])).
% 0.82/1.09 tff(4837,plain,
% 0.82/1.09 (~b(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1811, 272, 4826, 1805])).
% 0.82/1.09 tff(4838,plain,
% 0.82/1.09 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1766, 4837, 1647])).
% 0.82/1.09 tff(4839,plain,
% 0.82/1.09 ($false),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[2325, 371, 4808, 4838, 4836])).
% 0.82/1.09 tff(4840,plain,((~r(s(s(s(s(s(s(elem!1)))))), z)) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~r(z, s(elem!1))) | (s(s(elem!1)) = s(elem!1)) | (s(elem!1) = s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.09 tff(4841,plain,
% 0.82/1.09 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4840, 4800, 291, 4804, 262, 4767, 4793, 4803, 4781, 2372, 4772])).
% 0.82/1.09 tff(4842,plain,
% 0.82/1.09 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[562, 4841])).
% 0.82/1.09 tff(4843,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4844,plain,
% 0.82/1.09 (((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))) <=> ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4845,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4844])).
% 0.82/1.09 tff(4846,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(transitivity,[status(thm)],[4845, 4843])).
% 0.82/1.09 tff(4847,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(quant_inst,[status(thm)],[])).
% 0.82/1.09 tff(4848,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(elem!1)), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.09 inference(modus_ponens,[status(thm)],[4847, 4846])).
% 0.82/1.09 tff(4849,plain,
% 0.82/1.09 ($false),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4848, 272, 1030, 1586, 1805])).
% 0.82/1.09 tff(4850,plain,((~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.09 tff(4851,plain,
% 0.82/1.09 (~b(s(s(elem!1)), z)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4850, 4842, 4800])).
% 0.82/1.09 tff(4852,plain,
% 0.82/1.09 (r(s(s(elem!1)), z)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[453, 4851])).
% 0.82/1.09 tff(4853,plain,
% 0.82/1.09 (~r(s(s(elem!1)), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1222, 4852, 415])).
% 0.82/1.09 tff(4854,plain,
% 0.82/1.09 (b(s(s(elem!1)), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[660, 4853, 2372])).
% 0.82/1.09 tff(4855,plain,
% 0.82/1.09 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1618, 4854, 4803])).
% 0.82/1.09 tff(4856,plain,
% 0.82/1.09 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[527, 4855, 4773])).
% 0.82/1.09 tff(4857,plain,
% 0.82/1.09 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4788, 371, 4856, 4781])).
% 0.82/1.09 tff(4858,plain,
% 0.82/1.09 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1723, 4857])).
% 0.82/1.09 tff(4859,plain,
% 0.82/1.09 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1766, 1812, 1457])).
% 0.82/1.09 tff(4860,plain,
% 0.82/1.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4861,plain,
% 0.82/1.09 (((~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))) <=> ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4862,plain,
% 0.82/1.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4861])).
% 0.82/1.09 tff(4863,plain,
% 0.82/1.09 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(transitivity,[status(thm)],[4862, 4860])).
% 0.82/1.09 tff(4864,plain,
% 0.82/1.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.09 inference(quant_inst,[status(thm)],[])).
% 0.82/1.09 tff(4865,plain,
% 0.82/1.09 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.09 inference(modus_ponens,[status(thm)],[4864, 4863])).
% 0.82/1.09 tff(4866,plain,
% 0.82/1.09 ($false),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4865, 371, 1019, 4859, 2160])).
% 0.82/1.09 tff(4867,plain,((~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), z)) | (s(s(elem!1)) = s(s(s(s(s(s(s(elem!1)))))))) | (~b(z, elem!1)) | (~b(z, s(s(s(s(s(s(elem!1)))))))) | (~b(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.09 tff(4868,plain,
% 0.82/1.09 (~b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4867, 4852, 4794, 262, 4858, 4800])).
% 0.82/1.09 tff(4869,plain,
% 0.82/1.09 (r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1706, 4868, 4795])).
% 0.82/1.09 tff(4870,plain,
% 0.82/1.09 (~r(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[2280, 4869, 4793])).
% 0.82/1.09 tff(4871,plain,
% 0.82/1.09 (b(s(s(s(s(s(s(s(elem!1))))))), elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1690, 4870, 4767])).
% 0.82/1.09 tff(4872,plain,
% 0.82/1.09 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[2461, 4871, 291])).
% 0.82/1.09 tff(4873,plain,
% 0.82/1.09 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1847, 4869, 4856])).
% 0.82/1.09 tff(4874,plain,
% 0.82/1.09 ($false),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1699, 139, 4804, 4873, 4872])).
% 0.82/1.09 tff(4875,plain,((~b(z, elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.09 tff(4876,plain,
% 0.82/1.09 ((~b(z, elem!1)) | (s(s(elem!1)) = elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4875, 4740])).
% 0.82/1.09 tff(4877,plain,
% 0.82/1.09 (s(s(elem!1)) = elem!1),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4876, 262])).
% 0.82/1.09 tff(4878,plain,
% 0.82/1.09 (s(s(s(s(s(s(elem!1)))))) = elem!1),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[230, 4877])).
% 0.82/1.09 tff(4879,plain,
% 0.82/1.09 (s(s(s(s(s(s(s(elem!1))))))) = s(s(s(elem!1)))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[3624, 4877, 4878])).
% 0.82/1.09 tff(4880,plain,
% 0.82/1.09 (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[2232, 4879])).
% 0.82/1.09 tff(4881,plain,
% 0.82/1.09 (~(s(z) = elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[172, 4880])).
% 0.82/1.09 tff(4882,plain,
% 0.82/1.09 (~(s(elem!1) = s(s(z)))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1418, 4881])).
% 0.82/1.09 tff(4883,plain,
% 0.82/1.09 ((~b(s(s(z)), elem!1)) | (s(elem!1) = s(s(z))) | (~b(z, elem!1))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[1213, 4740])).
% 0.82/1.09 tff(4884,plain,
% 0.82/1.09 (~b(s(s(z)), elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4883, 4882, 262])).
% 0.82/1.09 tff(4885,plain,
% 0.82/1.09 (r(s(s(z)), elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[476, 4884, 4760])).
% 0.82/1.09 tff(4886,plain,
% 0.82/1.09 (~(s(s(s(s(z)))) = elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[3637, 4878, 4877])).
% 0.82/1.09 tff(4887,plain,
% 0.82/1.09 (elem!1 = s(s(elem!1))),
% 0.82/1.09 inference(symmetry,[status(thm)],[4877])).
% 0.82/1.09 tff(4888,plain,
% 0.82/1.09 (s(elem!1) = s(s(s(elem!1)))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4887])).
% 0.82/1.09 tff(4889,plain,
% 0.82/1.09 (b(s(elem!1), elem!1) <=> b(s(s(s(elem!1))), elem!1)),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4888])).
% 0.82/1.09 tff(4890,plain,
% 0.82/1.09 (b(s(s(s(elem!1))), elem!1)),
% 0.82/1.09 inference(modus_ponens,[status(thm)],[4740, 4889])).
% 0.82/1.09 tff(4891,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4892,plain,
% 0.82/1.09 (((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.82/1.09 inference(rewrite,[status(thm)],[])).
% 0.82/1.09 tff(4893,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4892])).
% 0.82/1.09 tff(4894,plain,
% 0.82/1.09 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.82/1.09 inference(transitivity,[status(thm)],[4893, 4891])).
% 0.82/1.09 tff(4895,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1))))))),
% 0.82/1.09 inference(quant_inst,[status(thm)],[])).
% 0.82/1.09 tff(4896,plain,
% 0.82/1.09 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(elem!1))), elem!1)) | (~b(s(s(s(s(z)))), elem!1)) | (~b(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.82/1.09 inference(modus_ponens,[status(thm)],[4895, 4894])).
% 0.82/1.09 tff(4897,plain,
% 0.82/1.09 (~b(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4896, 272, 4890, 4098])).
% 0.82/1.09 tff(4898,assumption,(s(s(s(s(z)))) = s(s(s(elem!1)))), introduced(assumption)).
% 0.82/1.09 tff(4899,plain,
% 0.82/1.09 (inj_0(s(s(s(s(z))))) = inj_0(s(s(s(elem!1))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[4898])).
% 0.82/1.09 tff(4900,plain,
% 0.82/1.09 (inj_0(s(s(s(elem!1)))) = inj_0(s(s(s(s(z)))))),
% 0.82/1.09 inference(symmetry,[status(thm)],[4899])).
% 0.82/1.09 tff(4901,plain,
% 0.82/1.09 (elem!1 = s(s(s(z)))),
% 0.82/1.09 inference(transitivity,[status(thm)],[3614, 602, 4900, 3609])).
% 0.82/1.09 tff(4902,plain,
% 0.82/1.09 ((~(s(s(s(z))) = elem!1)) <=> (~(elem!1 = s(s(s(z)))))),
% 0.82/1.09 inference(monotonicity,[status(thm)],[3664])).
% 0.82/1.09 tff(4903,plain,
% 0.82/1.09 ((s(s(s(z))) = z) <=> (elem!1 = z)),
% 0.82/1.09 inference(monotonicity,[status(thm)],[3665])).
% 0.82/1.09 tff(4904,plain,
% 0.82/1.09 ((s(s(s(z))) = z) <=> (z = elem!1)),
% 0.82/1.09 inference(transitivity,[status(thm)],[4903, 2])).
% 0.82/1.09 tff(4905,plain,
% 0.82/1.09 ((z = elem!1) <=> (s(s(s(z))) = z)),
% 0.82/1.09 inference(symmetry,[status(thm)],[4904])).
% 0.82/1.09 tff(4906,plain,
% 0.82/1.09 (elem!1 = s(s(s(z)))),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[3669, 3665])).
% 0.82/1.09 tff(4907,plain,
% 0.82/1.09 (~(s(s(elem!1)) = elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[3662, 4906])).
% 0.82/1.09 tff(4908,plain,
% 0.82/1.09 (~b(z, elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[4876, 4907])).
% 0.82/1.09 tff(4909,assumption,(~r(s(elem!1), elem!1)), introduced(assumption)).
% 0.82/1.09 tff(4910,plain,
% 0.82/1.09 (b(s(elem!1), elem!1)),
% 0.82/1.09 inference(unit_resolution,[status(thm)],[618, 2373, 4909])).
% 0.82/1.09 tff(4911,plain,
% 0.82/1.09 (b(s(s(elem!1)), s(z)) <=> b(s(s(elem!1)), elem!1)),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.10 tff(4912,plain,
% 0.82/1.10 (b(s(s(elem!1)), elem!1) <=> b(s(s(elem!1)), s(z))),
% 0.82/1.10 inference(symmetry,[status(thm)],[4911])).
% 0.82/1.10 tff(4913,plain,
% 0.82/1.10 ((s(z) = z) <=> (elem!1 = z)),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.10 tff(4914,plain,
% 0.82/1.10 ((s(z) = z) <=> (z = elem!1)),
% 0.82/1.10 inference(transitivity,[status(thm)],[4913, 2])).
% 0.82/1.10 tff(4915,plain,
% 0.82/1.10 ((~(s(z) = z)) <=> (~(z = elem!1))),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4914])).
% 0.82/1.10 tff(4916,plain,
% 0.82/1.10 (~(z = elem!1)),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[284, 4915])).
% 0.82/1.10 tff(4917,plain,
% 0.82/1.10 (~b(z, elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4875, 291, 233])).
% 0.82/1.10 tff(4918,plain,
% 0.82/1.10 (r(z, elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[432, 4917, 4916])).
% 0.82/1.10 tff(4919,plain,
% 0.82/1.10 (r(s(z), z) <=> r(elem!1, z)),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4764])).
% 0.82/1.10 tff(4920,plain,
% 0.82/1.10 (b(s(elem!1), s(z)) <=> b(s(elem!1), elem!1)),
% 0.82/1.10 inference(monotonicity,[status(thm)],[53])).
% 0.82/1.10 tff(4921,plain,
% 0.82/1.10 (b(s(elem!1), elem!1) <=> b(s(elem!1), s(z))),
% 0.82/1.10 inference(symmetry,[status(thm)],[4920])).
% 0.82/1.10 tff(4922,plain,
% 0.82/1.10 (b(s(elem!1), s(z))),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[291, 4921])).
% 0.82/1.10 tff(4923,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[319, 4922])).
% 0.82/1.10 tff(4924,plain,((~b(s(elem!1), elem!1)) | b(s(elem!1), s(z)) | (~(s(z) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4925,plain,
% 0.82/1.10 (b(s(elem!1), s(z))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4924, 291, 4764])).
% 0.82/1.10 tff(4926,plain,
% 0.82/1.10 (~b(s(z), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1316, 399, 4925])).
% 0.82/1.10 tff(4927,plain,
% 0.82/1.10 (r(s(z), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[289, 4926])).
% 0.82/1.10 tff(4928,plain,
% 0.82/1.10 (r(elem!1, z)),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[4927, 4919])).
% 0.82/1.10 tff(4929,plain,
% 0.82/1.10 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[522, 514, 291])).
% 0.82/1.10 tff(4930,plain,
% 0.82/1.10 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[545, 4929, 221])).
% 0.82/1.10 tff(4931,plain,
% 0.82/1.10 (~r(s(s(s(s(s(s(elem!1)))))), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1929, 4930, 972])).
% 0.82/1.10 tff(4932,plain,
% 0.82/1.10 (b(s(s(s(s(s(s(elem!1)))))), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[562, 4931])).
% 0.82/1.10 tff(4933,plain,
% 0.82/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4934,plain,
% 0.82/1.10 (((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1)))) <=> ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4935,plain,
% 0.82/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z))))),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4934])).
% 0.82/1.10 tff(4936,plain,
% 0.82/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)))),
% 0.82/1.10 inference(transitivity,[status(thm)],[4935, 4933])).
% 0.82/1.10 tff(4937,plain,
% 0.82/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z)) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))))),
% 0.82/1.10 inference(quant_inst,[status(thm)],[])).
% 0.82/1.10 tff(4938,plain,
% 0.82/1.10 ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~b(s(s(s(s(s(s(elem!1)))))), z))),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[4937, 4936])).
% 0.82/1.10 tff(4939,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4938, 272, 399, 514, 4932])).
% 0.82/1.10 tff(4940,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), z)) | (~r(elem!1, z)) | (s(s(s(s(s(s(elem!1)))))) = elem!1) | (~b(s(elem!1), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4941,plain,
% 0.82/1.10 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4940, 399, 4928, 4771, 291])).
% 0.82/1.10 tff(4942,plain,
% 0.82/1.10 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[527, 4941, 4773])).
% 0.82/1.10 tff(4943,plain,
% 0.82/1.10 (r(s(s(elem!1)), s(z)) <=> r(s(s(elem!1)), elem!1)),
% 0.82/1.10 inference(monotonicity,[status(thm)],[53])).
% 0.82/1.10 tff(4944,plain,
% 0.82/1.10 (r(s(s(elem!1)), elem!1) <=> r(s(s(elem!1)), s(z))),
% 0.82/1.10 inference(symmetry,[status(thm)],[4943])).
% 0.82/1.10 tff(4945,plain,
% 0.82/1.10 ((~r(s(s(elem!1)), elem!1)) <=> (~r(s(s(elem!1)), s(z)))),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4944])).
% 0.82/1.10 tff(4946,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1963, 272, 717, 399, 1030])).
% 0.82/1.10 tff(4947,plain,((~b(s(s(elem!1)), z)) | (~b(s(s(elem!1)), s(elem!1))) | (~b(s(elem!1), z))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4948,plain,
% 0.82/1.10 (~b(s(s(elem!1)), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4947, 717, 399])).
% 0.82/1.10 tff(4949,plain,
% 0.82/1.10 (r(s(s(elem!1)), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[453, 4948])).
% 0.82/1.10 tff(4950,plain,
% 0.82/1.10 (~b(s(z), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1316, 399, 308])).
% 0.82/1.10 tff(4951,plain,
% 0.82/1.10 (r(s(z), z)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[289, 4950])).
% 0.82/1.10 tff(4952,plain,
% 0.82/1.10 (r(elem!1, z)),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[4951, 1483])).
% 0.82/1.10 tff(4953,plain,
% 0.82/1.10 (~r(s(s(elem!1)), elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1947, 371, 4952, 4949])).
% 0.82/1.10 tff(4954,plain,
% 0.82/1.10 (~r(s(s(elem!1)), s(z))),
% 0.82/1.10 inference(modus_ponens,[status(thm)],[4953, 4945])).
% 0.82/1.10 tff(4955,plain,
% 0.82/1.10 (~b(s(s(elem!1)), s(z))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1201, 717, 308])).
% 0.82/1.10 tff(4956,plain,
% 0.82/1.10 (r(s(s(elem!1)), s(z))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[890, 4955])).
% 0.82/1.10 tff(4957,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4956, 4954])).
% 0.82/1.10 tff(4958,plain,((~b(s(s(elem!1)), s(elem!1))) | (~(s(z) = elem!1)) | (~b(s(elem!1), z)) | (~b(s(elem!1), s(z)))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4959,plain,
% 0.82/1.10 (~b(s(s(elem!1)), s(elem!1))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4958, 399, 4764, 4925])).
% 0.82/1.10 tff(4960,plain,
% 0.82/1.10 (r(s(s(elem!1)), s(elem!1))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[660, 4959, 2372])).
% 0.82/1.10 tff(4961,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[2504, 371, 1215, 1842, 944])).
% 0.82/1.10 tff(4962,plain,((~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(elem!1)), s(elem!1))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4963,plain,
% 0.82/1.10 (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4962, 4960, 4942])).
% 0.82/1.10 tff(4964,assumption,(~b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.82/1.10 tff(4965,assumption,(~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), introduced(assumption)).
% 0.82/1.10 tff(4966,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[963, 139, 177, 4965, 4964])).
% 0.82/1.10 tff(4967,plain,(r(s(s(elem!1)), s(s(s(s(s(s(elem!1))))))) | (s(s(elem!1)) = s(s(s(s(s(s(elem!1))))))) | b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4968,plain,
% 0.82/1.10 (b(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4967, 4963, 4799])).
% 0.82/1.10 tff(4969,plain,
% 0.82/1.10 (~r(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1390, 371, 4960, 4942])).
% 0.82/1.10 tff(4970,plain,
% 0.82/1.10 (b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[611, 139, 4802, 4969])).
% 0.82/1.10 tff(4971,plain,
% 0.82/1.10 (~r(elem!1, s(s(elem!1)))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1493, 1019, 972])).
% 0.82/1.10 tff(4972,plain,
% 0.82/1.10 (b(elem!1, s(s(elem!1)))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1045, 4971, 96])).
% 0.82/1.10 tff(4973,plain,
% 0.82/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4974,plain,
% 0.82/1.10 (((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))) <=> ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4975,plain,
% 0.82/1.10 (((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1)))) <=> ((~![X0: $i, X3: $i, X2: $i, X1: $i] : ((~b(X1, X3)) | (~b(X0, X3)) | (~b(X1, X2)) | (~b(X0, X1)))) | ((~b(elem!1, s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), s(s(elem!1)))) | (~b(s(s(s(s(s(s(elem!1)))))), elem!1))))),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4974])).
% 0.82/1.10 tff(4976,plain,
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% 0.82/1.10 inference(transitivity,[status(thm)],[4975, 4973])).
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% 0.82/1.10 inference(quant_inst,[status(thm)],[])).
% 0.82/1.10 tff(4978,plain,
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% 0.82/1.10 inference(modus_ponens,[status(thm)],[4977, 4976])).
% 0.82/1.10 tff(4979,plain,
% 0.82/1.10 (~b(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4978, 272, 4972, 551])).
% 0.82/1.10 tff(4980,plain,
% 0.82/1.10 (r(s(s(s(s(s(s(elem!1)))))), elem!1)),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[545, 4979, 221])).
% 0.82/1.10 tff(4981,plain,
% 0.82/1.10 (~b(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[2461, 2282, 291])).
% 0.82/1.10 tff(4982,plain,
% 0.82/1.10 ($false),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1699, 139, 1696, 3022, 4981])).
% 0.82/1.10 tff(4983,plain,((~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))) | (s(s(s(s(s(s(s(elem!1))))))) = s(elem!1)) | (~b(s(elem!1), elem!1)) | (s(s(s(s(s(s(s(elem!1))))))) = elem!1) | (~r(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.82/1.10 tff(4984,plain,
% 0.82/1.10 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[4983, 4980, 291, 1652, 1842, 1658])).
% 0.82/1.10 tff(4985,plain,
% 0.82/1.10 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.10 inference(unit_resolution,[status(thm)],[1706, 4984, 1980])).
% 0.82/1.10 tff(4986,plain,
% 0.82/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4987,plain,
% 0.82/1.10 (((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(elem!1))))))))) <=> ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.10 inference(rewrite,[status(thm)],[])).
% 0.82/1.10 tff(4988,plain,
% 0.82/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.10 inference(monotonicity,[status(thm)],[4987])).
% 0.82/1.10 tff(4989,plain,
% 0.82/1.10 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(z, elem!1)) | (~r(s(s(s(s(s(s(elem!1)))))), elem!1)) | (~r(z, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.10 inference(transitivity,[status(thm)],[4988, 4986])).
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% 0.82/1.11 inference(rewrite,[status(thm)],[])).
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% 0.82/1.11 inference(modus_ponens,[status(thm)],[5104, 5103])).
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% 0.82/1.12 inference(rewrite,[status(thm)],[])).
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% 0.82/1.12 inference(rewrite,[status(thm)],[])).
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% 0.82/1.12 inference(modus_ponens,[status(thm)],[5170, 5169])).
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% 0.82/1.12 inference(modus_ponens,[status(thm)],[5200, 5199])).
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% 0.82/1.12 (r(elem!1, s(s(s(s(s(s(elem!1)))))))),
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% 0.82/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.12 inference(rewrite,[status(thm)],[])).
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% 0.82/1.12 inference(rewrite,[status(thm)],[])).
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% 0.82/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))))),
% 0.82/1.12 inference(monotonicity,[status(thm)],[5207])).
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% 0.82/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1)))))))))),
% 0.82/1.12 inference(transitivity,[status(thm)],[5208, 5206])).
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% 0.82/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(elem!1, s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(s(s(elem!1)), elem!1)))),
% 0.82/1.12 inference(quant_inst,[status(thm)],[])).
% 0.82/1.12 tff(5211,plain,
% 0.82/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(s(elem!1)), elem!1)) | (~r(s(s(elem!1)), s(s(s(s(s(s(elem!1)))))))) | (~r(elem!1, s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.12 inference(modus_ponens,[status(thm)],[5210, 5209])).
% 0.82/1.12 tff(5212,plain,
% 0.82/1.12 (~r(s(s(elem!1)), elem!1)),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[5211, 371, 5205, 5121])).
% 0.82/1.12 tff(5213,plain,
% 0.82/1.12 (b(s(s(elem!1)), elem!1)),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[843, 5212, 233])).
% 0.82/1.12 tff(5214,plain,
% 0.82/1.12 (r(s(s(elem!1)), s(s(s(s(s(s(s(elem!1))))))))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[2212, 5188, 5205, 4767, 5121, 4794, 5213])).
% 0.82/1.12 tff(5215,plain,
% 0.82/1.12 ($false),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[1761, 5214, 5189, 5121])).
% 0.82/1.12 tff(5216,plain,((~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))) | (~b(s(elem!1), elem!1)) | (s(s(elem!1)) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.82/1.12 tff(5217,plain,
% 0.82/1.12 (~b(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[5216, 4910, 233])).
% 0.82/1.12 tff(5218,plain,
% 0.82/1.12 (r(s(s(s(s(s(s(elem!1)))))), s(elem!1))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[527, 5217, 4773])).
% 0.82/1.12 tff(5219,plain,
% 0.82/1.12 (~r(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[4983, 5218, 4910, 4767, 5089, 4804])).
% 0.82/1.12 tff(5220,plain,
% 0.82/1.12 (b(s(s(s(s(s(s(s(elem!1))))))), s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[1706, 5219, 4795])).
% 0.82/1.12 tff(5221,plain,
% 0.82/1.12 (~b(z, elem!1)),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[4875, 4910, 233])).
% 0.82/1.12 tff(5222,plain,
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% 0.82/1.12 inference(unit_resolution,[status(thm)],[432, 5221, 4916])).
% 0.82/1.12 tff(5223,plain,
% 0.82/1.12 (~r(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[4991, 371, 5222, 5089])).
% 0.82/1.12 tff(5224,plain,
% 0.82/1.12 (b(z, s(s(s(s(s(s(elem!1)))))))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[1723, 5223])).
% 0.82/1.12 tff(5225,plain,
% 0.82/1.12 (~b(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[4999, 272, 5224, 5220])).
% 0.82/1.12 tff(5226,plain,
% 0.82/1.12 (r(s(s(s(s(s(s(s(elem!1))))))), z)),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[1734, 139, 170, 5225])).
% 0.82/1.12 tff(5227,plain,
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% 0.82/1.12 inference(unit_resolution,[status(thm)],[5047, 4910, 233])).
% 0.82/1.12 tff(5228,plain,
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% 0.82/1.12 inference(unit_resolution,[status(thm)],[414, 5227])).
% 0.82/1.12 tff(5229,plain,
% 0.82/1.12 (((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))) <=> ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.82/1.12 inference(rewrite,[status(thm)],[])).
% 0.82/1.12 tff(5230,plain,
% 0.82/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | ((~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))))),
% 0.82/1.12 inference(quant_inst,[status(thm)],[])).
% 0.82/1.12 tff(5231,plain,
% 0.82/1.12 ((~![X0: $i, X2: $i, X1: $i] : ((~r(X1, X2)) | (~r(X0, X2)) | (~r(X0, X1)))) | (~r(s(elem!1), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), z)) | (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1)))),
% 0.82/1.12 inference(modus_ponens,[status(thm)],[5230, 5229])).
% 0.82/1.12 tff(5232,plain,
% 0.82/1.12 (~r(s(s(s(s(s(s(s(elem!1))))))), s(elem!1))),
% 0.82/1.12 inference(unit_resolution,[status(thm)],[5231, 371, 5228, 5226])).
% 0.82/1.12 tff(5233,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[1699, 139, 4804, 5232])).
% 0.91/1.13 tff(5234,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[2461, 5233, 4910])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[1690, 5234, 4767])).
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% 0.91/1.13 tff(5237,plain,((s(s(elem!1)) = elem!1) | r(s(elem!1), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(5238,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[5237, 4907])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[5047, 4740])).
% 0.91/1.13 tff(5240,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[5239, 4907])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[414, 5240])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[828, 5241, 5238])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[432, 5242, 4908])).
% 0.91/1.13 tff(5244,plain,
% 0.91/1.13 (s(s(s(z))) = z),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[5243, 4905])).
% 0.91/1.13 tff(5245,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[1535, 5244])).
% 0.91/1.13 tff(5246,plain,(~(s(s(s(z))) = elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(5247,plain,
% 0.91/1.13 (~(elem!1 = s(s(s(z))))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[5246, 4902])).
% 0.91/1.13 tff(5248,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[5247, 4901])).
% 0.91/1.13 tff(5249,plain,((~(s(s(s(s(z)))) = s(s(s(elem!1))))) | (~(s(s(elem!1)) = elem!1))), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(5250,plain,
% 0.91/1.13 (~(s(s(s(s(z)))) = s(s(s(elem!1))))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[5249, 4877])).
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% 0.91/1.13 (((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))) <=> ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.91/1.13 inference(rewrite,[status(thm)],[])).
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% 0.91/1.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | ((s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1)))))),
% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
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% 0.91/1.13 ((~![Y: $i, X: $i] : ((X = Y) | b(X, Y) | r(X, Y))) | (s(s(s(s(z)))) = s(s(s(elem!1)))) | b(s(s(s(s(z)))), s(s(s(elem!1)))) | r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.91/1.13 inference(modus_ponens,[status(thm)],[5252, 5251])).
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% 0.91/1.13 (r(s(s(s(s(z)))), s(s(s(elem!1))))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[5253, 139, 5250, 4897])).
% 0.91/1.13 tff(5255,plain,
% 0.91/1.13 (r(s(elem!1), z) <=> r(s(s(s(elem!1))), z)),
% 0.91/1.13 inference(monotonicity,[status(thm)],[4888])).
% 0.91/1.13 tff(5256,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[407, 4740])).
% 0.91/1.13 tff(5257,plain,
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[5256, 262])).
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% 0.91/1.13 inference(unit_resolution,[status(thm)],[414, 5257])).
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% 0.91/1.13 inference(modus_ponens,[status(thm)],[5258, 5255])).
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% 0.91/1.13 inference(quant_inst,[status(thm)],[])).
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% 0.91/1.13 inference(modus_ponens,[status(thm)],[5261, 5260])).
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% 0.91/1.13 (~r(z, s(s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1063, 5300, 5275])).
% 0.91/1.13 tff(5304,plain,
% 0.91/1.13 (b(z, s(s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1073, 5303])).
% 0.91/1.13 tff(5305,plain,
% 0.91/1.13 (~b(s(z), s(s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1379, 5304, 5302])).
% 0.91/1.13 tff(5306,plain,
% 0.91/1.13 (r(s(z), s(s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[804, 5305])).
% 0.91/1.13 tff(5307,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1359, 371, 5306, 5300, 5285])).
% 0.91/1.13 tff(5308,plain,(b(s(z), elem!1)), inference(lemma,lemma(discharge,[]))).
% 0.91/1.13 tff(5309,plain,
% 0.91/1.13 (~(s(elem!1) = s(s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1418, 5284])).
% 0.91/1.13 tff(5310,plain,
% 0.91/1.13 (~(s(elem!1) = s(z))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[1886, 4762])).
% 0.91/1.13 tff(5311,plain,
% 0.91/1.13 ((~b(s(z), elem!1)) | (~b(s(elem!1), s(z)))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[316, 4740])).
% 0.91/1.13 tff(5312,plain,
% 0.91/1.13 (~b(s(elem!1), s(z))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[5311, 5308])).
% 0.91/1.13 tff(5313,plain,
% 0.91/1.13 (r(s(elem!1), s(z))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[324, 5312, 5310])).
% 0.91/1.13 tff(5314,plain,
% 0.91/1.13 ((~b(s(s(z)), elem!1)) | (~r(s(elem!1), s(z))) | (s(elem!1) = s(s(z))) | (~b(s(z), elem!1))),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[379, 4740])).
% 0.91/1.13 tff(5315,plain,
% 0.91/1.13 (~b(s(s(z)), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[5314, 5313, 5309, 5308])).
% 0.91/1.13 tff(5316,plain,
% 0.91/1.13 (r(s(s(z)), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[476, 5315, 4760])).
% 0.91/1.13 tff(5317,plain,
% 0.91/1.13 (~r(s(s(s(s(z)))), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[4682, 5308, 5246, 5275, 4760])).
% 0.91/1.13 tff(5318,plain,
% 0.91/1.13 (b(s(s(s(s(z)))), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[4096, 5317, 5286])).
% 0.91/1.13 tff(5319,plain,
% 0.91/1.13 (~b(s(s(s(z))), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[4716, 5318, 5308])).
% 0.91/1.13 tff(5320,plain,
% 0.91/1.13 (r(s(s(s(z))), elem!1)),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[3993, 5319, 5246])).
% 0.91/1.13 tff(5321,plain,
% 0.91/1.13 ($false),
% 0.91/1.13 inference(unit_resolution,[status(thm)],[4723, 5320, 5316, 5275])).
% 0.91/1.13 % SZS output end Proof
% 0.91/1.13 % E exiting
%------------------------------------------------------------------------------